Exhibit 10.4

FORM OF NON-REDEMPTION AGREEMENT

THIS NON-REDEMPTION AGREEMENT (this “Agreement”), dated as of _____________, 2025, is made by and between Helix Acquisition Corp. II, a Cayman Islands exempted company (the “Company”), and the undersigned shareholder (the “Holder”).

RECITALS

WHEREAS, substantially concurrently with the execution of this Agreement, the Company is entering into a business combination agreement (as amended, supplemented, restated or otherwise modified from time to time, the “Business Combination Agreement”), with TheRas, Inc. (doing business as BridgeBio Oncology Therapeutics) (“BBOT”) and Helix II Merger Sub, Inc., a Delaware corporation and wholly-owned subsidiary of the Company (“Merger Sub”), pursuant to which (and subject to the terms and conditions set forth therein) the Company will de-register in the Cayman Islands and transfer by way of continuation out of the Cayman Islands and into the State of Delaware so as to migrate to and domesticate as a Delaware corporation in accordance with Section 388 of the Delaware General Corporation Law, as amended, and Part XII of the Companies Act (As Revised) of the Cayman Islands (the “Domestication”), and, promptly thereafter, Merger Sub will merge with and into BBOT, with BBOT surviving the merger as a wholly-owned subsidiary of the Company (the “Merger,” and together with the Domestication and the other transactions contemplated by the Business Combination Agreement, the “Transactions”);

WHEREAS, the Company’s amended and restated memorandum and articles of association (the “Articles”) provides that a shareholder of the Company may redeem its Class A ordinary shares, par value $0.0001 per share (whether they were purchased in the Company’s initial public offering or thereafter in the open market) (the “Public Shares”), in connection with the consummation of the Transactions, on the terms set forth in the Articles (“Redemption Rights”); and

WHEREAS, Holder wishes to waive its Redemption Rights with respect to [●] Public Shares held by it and/or its controlled affiliates as of the date hereof (the “Holder’s Shares”), to agree to hold the Holder’s Shares through the consummation of the Transactions (the date that the Transactions are consummated, the “Closing Date”), and to agree to vote the Holder’s Shares in favor of the Transactions and related matters set forth herein.

NOW, THEREFORE, in consideration of the foregoing and the mutual acknowledgments, understandings, and agreements contained in this Agreement and for other good and valuable consideration, the receipt and adequacy of which are hereby acknowledged, the Company and Holder hereby agree as follows:

(a) Holder and/or certain of its controlled affiliates beneficially own the Holder’s Shares.

(b) Holder (i) is a legal entity duly organized, validly existing and, to the extent such concept is applicable, in good standing under the laws of the jurisdiction of its organization and (ii) has all requisite corporate or other power and authority and has taken all corporate or other action necessary in order to execute, deliver and perform its obligations under this Agreement and to consummate the transactions contemplated hereby. This Agreement has been authorized, duly executed and delivered by Holder and, assuming due authorization and execution by the Company, constitutes the valid and binding agreement of Holder, enforceable against Holder in accordance with its terms, subject to applicable bankruptcy, insolvency, fraudulent conveyance, reorganization, moratorium and similar laws affecting creditors’ rights generally and subject, as to enforceability, to general principles of equity.

(c) The execution and delivery of this Agreement by Holder do not, and the performance by Holder of its obligations hereunder will not, (i) conflict with or result in a violation of the organizational documents of Holder (if applicable) or applicable law to which Holder or the Holder’s Shares is subject, or (ii) require any consent or approval that has not been given or other action that has not been taken by any person (including under any contract binding upon Holder or any Holder’s Shares), in each case, to the extent such consent, approval, or other action would prevent, enjoin or materially delay the performance by Holder of its obligations under this Agreement.

(d) As of the date of this Agreement, (i) there is no action, claim, suit, audit, assessment, arbitration, mediation or inquiry, or any proceeding or investigation, by or before any governmental authority pending against Holder or, to the knowledge of Holder, threatened against Holder and (ii) Holder is not a party to or subject to the provisions of any order, judgment, injunction, decree, writ, stipulation, determination or award, in each case, entered by or with any governmental authority, in each case, that questions the beneficial or record ownership of the Holder’s Shares or the validity of this Agreement or would reasonably be expected to prevent or materially delay, impair or adversely affect the performance by Holder of its obligations under this Agreement.

(e) The Holder is capable of assessing the merits of and understanding (on its own behalf or through independent professional advice), and understands and accepts, the terms, conditions and risks of this Agreement and the transactions contemplated hereby. Holder is also capable of assuming, and assumes, the risks of this Agreement and the transactions contemplated hereby. Holder is a sophisticated investor, capable of evaluating investment risks independently, both in general and with regard to all transactions and investment strategies involving a security or securities. The Holder has adequately analyzed and fully considered the risks of this Agreement and the transactions contemplated hereby and has determined that the transactions contemplated by this Agreement are suitable for the Holder and that the Holder is able at this time and in the foreseeable future to bear the economic risk of a total loss of its investment in the Company. The Holder acknowledges specifically that a possibility of total loss of its investment exists.

(a) Holder acknowledges that it has Redemption Rights with respect to the Holder’s Shares pursuant to the Articles. Holder hereby irrevocably and unconditionally covenants and agrees, for the benefit of the Company, that neither it nor any of its controlled affiliates shall exercise any Redemption Rights under the Articles with respect to the Holder’s Shares at any meeting of the shareholders of the Company, however called, or at any adjournment or postponement thereof, or in any other circumstance in which the vote, consent or other approval of the shareholders of the Company is sought.

(b) Holder shall not directly or indirectly Transfer the Holder’s Shares at any time during the period beginning on the date hereof and ending on the earlier of (x) the Closing Date, (y) the termination of the Business Combination Agreement in accordance with its terms and (z) the termination of this Agreement in accordance with Section 5(a). As used herein, “Transfer” or “Transferred” shall mean the following: (i) sale of, offer to sell, contract or agreement to sell, gift, hypothecate, place a lien on, pledge, lend, assign, grant of any option to purchase or otherwise dispose of or agreement to dispose of, directly or indirectly, or establishment or increase of a put equivalent position or liquidation with respect to or decrease of a call equivalent position within the meaning of Section 16 of the Securities Exchange Act of 1934, as amended, and the rules and regulations of the United States Securities and Exchange Commission (“SEC”) promulgated thereunder with respect to, any of the Holder’s Shares; (ii) engage in any hedging or other transaction or arrangement (including, without limitation, any short sale or the purchase or sale of, or entry into, any put or call option, or combination thereof, forward, swap or any other derivative transaction or instrument, however described or defined) which is designed to or which reasonably could be expected to lead to or result in a sale, loan, pledge or other disposition (whether by the undersigned or someone other than the undersigned), or transfer of any of the economic consequences of ownership, in whole or in part, directly or indirectly, of any Holder’s Shares, whether any such transaction or arrangement (or instrument provided for thereunder) would be settled by delivery of Holder’s Shares or other securities, in cash or otherwise or (iii) public announcement of any intention to effect any transaction specified in clause (i) or (ii). Notwithstanding anything to the contrary set forth herein, (i) nothing in this Section 2(b) shall prohibit any entities under common management or that share an investment adviser with Holder from effecting any Transfer of securities of the Company; and if Holder is a multi-managed investment vehicle whereby separate portfolio managers manage separate portions of Holder’s assets, this Section 2(b) shall only apply with respect to the portion of assets managed by the portfolio manager that made the investment decision to enter into this Agreement. The Company acknowledges and agrees that, notwithstanding anything herein to the contrary, the Holder’s Shares may be pledged by Holder in connection with a bona fide margin agreement, provided that such pledge shall be (i) pursuant to an available exemption from the registration requirements of the Securities Act or (ii) pursuant to, and in accordance with, a registration statement that is effective under the Securities Act at the time of such pledge, and Holder effecting a pledge of the Holder’s Shares shall not be required to provide the Company with any notice thereof; provided, however, that neither the Company nor its counsel shall be required to take any action (or refrain from taking any action) in connection with any such pledge, other than providing any such lender of such margin agreement with an acknowledgment that, if true, the Holder’s Shares are not subject to any contractual lock up or prohibition on pledging, the form of such acknowledgment to be subject to review and comment by the Company in all respects.

(c) In furtherance of the covenants in Sections 2(a) and 2(b): (x) Holder hereby irrevocably and unconditionally waives, on behalf of itself and its controlled affiliates, the Redemption Rights, and irrevocably and unconditionally constitutes and appoints the Company and its designees, with full power of substitution, as its (and its controlled affiliates’) true and lawful agent and attorney-in-fact, with full power and authority in its name, place and stead, to revoke any redemption election made in contravention of Section 2(a) above with respect to any Holder’s Shares and to cause the Company’s transfer agent to fail to redeem such Holder’s Shares, (y) Holder shall deliver such documentation as is reasonably requested by the Company to evidence that none of the Holder’s Shares have been redeemed or Transferred, and (z) in the event of a breach of Section 2(a) or 2(b) with respect to any Holder’s Shares (the “Transferred/Redeemed Shares”), Holder irrevocably and unconditionally agrees to, or to cause one or more of its affiliates to, subscribe for and purchase from the Company (or from its assignee(s) or designee(s)) prior to the Domestication a number of Class A ordinary shares of the Company equal to the number of such Transferred/Redeemed Shares, for a per share purchase price equal to the amount to be received by public shareholders of the Company exercising their Redemption Rights in connection with the Transactions.

(d) The Company acknowledges and agrees that the Holder and/or its controlled affiliates may own additional Public Shares in excess of the Holder’s Shares (the “Other Shares”) and that nothing herein shall restrict any rights of the Holder with respect to such Other Shares including, without limitation, the Redemption Rights or to otherwise exercise any right with respect to such Other Shares or to Transfer or vote such Other Shares.

3. Agreement to Vote.

(a) At any meeting of the shareholders of the Company, however called, or at any adjournment or postponement thereof, or in any other circumstance in which the vote, consent or other approval of the shareholders of the Company is sought, Holder and its controlled affiliates shall appear at each such meeting or otherwise cause all of the Holder’s Shares to be counted as present thereat for purposes of calculating a quorum and vote (or cause to be voted), or execute and deliver a written consent (or cause a written consent to be executed and delivered) covering, all of such Holder’s Shares (i) in favor of the Business Combination Agreement, the Domestication and Merger and each other proposal brought by the Company in connection with the Transactions and (ii) in favor of any proposal brought by the Company to adjourn or postpone the shareholder meeting called in connection with the Transactions.

(b) Holder (i) shall not enter into, at any time while this Agreement remains in effect, any voting agreement or voting trust with respect to the Holder’s Shares and (ii) shall not grant, at any time while this Agreement remains in effect, a proxy, consent or power of attorney with respect to the Holder’s Shares that is inconsistent with this Agreement.

4. Covenants of the Holder. Holder hereby agrees to permit the Company to publish and disclose Holder’s identity, ownership of the Holder’s Shares and any Other Shares and the nature of Holder’s commitments, arrangements and understandings under this Agreement and a copy of this Agreement, in (a) the registration statement, proxy statement, prospectus, and other proxy materials filed by the Company with the SEC in connection with the Transactions, (b) any Form 8-K and/or any periodic report filed by the Company with the SEC in connection with the execution and delivery of this Agreement, or in connection with the Transactions, and (c) any other documents or communications provided by the Company or the Company to any governmental authority, stock exchange, or to the Company’s shareholders, in each case, to the extent required by the federal securities laws or the SEC or any other securities authorities. Holder agrees that it shall not, and shall cause its affiliates not to, indirectly accomplish or attempt to accomplish that which it is not permitted to accomplish directly under this Agreement. Holder shall take, or cause to be taken, all actions and do, or cause to be done, all things reasonably necessary under applicable law to effect the actions set forth herein and to consummate the transactions contemplated hereby on the terms and subject to the conditions set forth herein. While this Agreement is in effect, Holder shall not (x) enter into any agreement that would restrict, limit or interfere with the performance of Holder’s obligations hereunder or (y) take any action that would make any representation or warranty of the Holder contained herein untrue or inaccurate in any material respect or have the effect of preventing or disabling Holder from performing any of its obligations under this Agreement.

5. Miscellaneous.

(a) This Agreement shall terminate and be void and of no further force and effect, and all rights and obligations of the parties hereunder shall terminate without any further liability on the part of any party in respect thereof, on the earliest to occur of (i) the Closing Date, (ii) on such date and time as the Business Combination Agreement is terminated in accordance with its terms, (iii) the mutual written agreement of the parties hereto to terminate this Agreement, (iv) on the date that is 60 days after the Outside Closing Date (as defined in the Business Combination Agreement), or (v) upon the liquidation of the Company.

(b) Holder acknowledges that the Company will rely on the representations, warranties, acknowledgments, understandings and agreements contained in this Agreement. Holder agrees to promptly notify the Company if any of the representations, warranties, acknowledgments, understandings or agreements set forth herein are no longer accurate in all material respects.

(c) Each of the Company and the Holder is entitled to rely upon this Agreement and is irrevocably authorized to produce this Agreement or a copy hereof to any interested party in any administrative or legal proceeding or official inquiry with respect to the matters covered hereby.

(d) Other than as specifically set forth herein, each party shall pay all of its own expenses in connection with this Agreement and the transactions contemplated hereby.

(e) Neither this Agreement nor any rights that may accrue to Holder hereunder may be transferred or assigned by the Holder. Neither this Agreement nor any rights that may accrue to the Company hereunder may be transferred or assigned, except to BBOT in connection with the consummation of the Transactions.

(f) This Agreement may not be amended, modified, supplemented, or waived except by an instrument in writing, signed by the party against whom enforcement of such amendment, modification, supplement, or waiver is sought.

(g) This Agreement constitutes the entire agreement, and supersedes all other prior agreements, understandings, representations and warranties, both written and oral, among the parties, with respect to the subject matter hereof.

(h) Except as otherwise provided herein, this Agreement shall be binding upon, and inure to the benefit of the parties hereto and their heirs, executors, administrators, successors, legal representatives, and permitted assigns, and the agreements, representations, warranties, covenants and acknowledgments contained herein shall be deemed to be made by, and be binding upon, such heirs, executors, administrators, successors, legal representatives and permitted assigns. Except as set forth in Section 5(e), this Agreement shall not confer any rights or remedies upon any person other than the parties hereto and their respective successors and assigns.

(i) Holder acknowledges that the Company has established a trust account containing the proceeds of its initial public offering and from certain private placements (collectively, with interest accrued from time to time thereon, the “Trust Account”). Holder agrees that (i) it has no right, title, interest or claim of any kind in or to any monies held in the Trust Account, and (ii) it shall have no right of set-off or any right, title, interest or claim of any kind (“Claim”) to, or to any monies in, the Trust Account, in each case in connection with this Agreement, and hereby irrevocably and unconditionally waives any Claim to, or to any monies in, the Trust Account that it may have in connection with this Agreement or otherwise; provided, that such release and waiver of Claims shall not include any rights or claims of Holder or any of its controlled affiliates to exercise Redemption Rights with respect to the Other Shares. In the event Holder has any Claim against the Company, Holder shall pursue such Claim solely against the Company’s assets outside the Trust Account and not against the property or any monies in the Trust Account. Holder agrees and acknowledges that such waiver is material to this Agreement and has been specifically relied upon by the Company to induce the Company to enter into this Agreement and Holder further intends and understands such waiver to be valid, binding and enforceable under applicable law.

(j) No failure or delay by a party hereto in exercising any right, power or remedy under this Agreement, and no course of dealing between the parties hereto, shall operate as a waiver of any such right, power or remedy of such party. No single or partial exercise of any right, power or remedy under this Agreement by a party hereto, nor any abandonment or discontinuance of steps to enforce any such right, power or remedy, shall preclude such party from any other or further exercise thereof or the exercise of any other right, power or remedy hereunder. The election of any remedy by a party hereto shall not constitute a waiver of the right of such party to pursue other available remedies. No notice to or demand on a party not expressly required under this Agreement shall entitle the party receiving such notice or demand to any other or further notice or demand in similar or other circumstances or constitute a waiver of the rights of the party giving such notice or demand to any other or further action in any circumstances without such notice or demand.

(k) This Agreement may be executed in one or more counterparts (including by facsimile or electronic mail or in .pdf), and by different parties in separate counterparts, with the same effect as if all parties hereto had signed the same document. All counterparts so executed and delivered shall be construed together and shall constitute one and the same agreement.

(l) Any notice or communication required or permitted hereunder shall be in writing and either delivered personally, emailed, sent by overnight mail via a reputable overnight carrier, or sent by certified or registered mail, postage prepaid, and shall be deemed to be given and received (a) when so delivered personally, (b) when sent, with no mail undeliverable or other rejection notice, if sent by email, or (c) five (5) business days after the date of mailing to the address below or to such other address or addresses as such person may hereafter designate by notice given hereunder:

If to Holder, to such address or addresses set forth on the signature page hereto;

If to the Company, to:

Helix Acquisition Corp. II
c/o Cormorant Asset Management, LP
200 Clarendon Street, 52nd Floor
Boston, MA 02116
Attn: Bihua Chen
E-mail: chen@cormorant-asset.com

with a copy (which shall not constitute notice) to:

White & Case LLP
1221 Avenue of the Americas
New York, New York 10020
Attention: Joel L. Rubinstein
E-mail: joel.rubinstein@whitecase.com

(m) The parties hereto acknowledge and agree that (i) this Agreement is being entered into in order to induce the Company to execute and deliver the Business Combination Agreement and (ii) immediate and irreparable harm or damage would occur in the event that any of the provisions of this Agreement were not performed in accordance with their specific terms or were otherwise breached and that money or other legal remedies would not be an adequate remedy for such damage. It is accordingly agreed that the Company shall be entitled to equitable relief, including in the form of an injunction or injunctions to prevent breaches or threatened breaches or restraining any violation or threatened violation of this Agreement and to enforce specifically the terms and provisions of this Agreement in the Designated Courts pursuant to Section 5(p), this being in addition to any other remedy to which the Company is entitled at law, in equity, in contract, in tort or otherwise. The parties hereto acknowledge and agree that the Company shall be entitled to specifically enforce Holder’s obligations hereunder, in each case, on the terms and subject to the conditions set forth herein. The parties hereto further acknowledge and agree: (x) to waive any requirement for the security or posting of any bond in connection with any such equitable remedy; (y) not to assert that a remedy of specific enforcement pursuant to this Section 5(m) is unenforceable, invalid, contrary to applicable law or inequitable for any reason; and (z) to waive any defenses in any action for specific performance, including the defense that a remedy at law would be adequate.

(n) This Agreement, and all claims or causes of action based upon, arising out of, or related to this Agreement or the transactions contemplated hereby, shall be governed by, and construed in accordance with, the laws of the State of Delaware, without giving effect to principles or rules of conflict of laws to the extent such principles or rules would require or permit the application of laws of another jurisdiction.

(o) EACH PARTY AND ANY PERSON ASSERTING RIGHTS AS A THIRD PARTY BENEFICIARY HEREBY WAIVES ITS RESPECTIVE RIGHTS TO A TRIAL BY JURY OF ANY CLAIM OR CAUSE OF ACTION BASED UPON OR ARISING OUT OR RELATED TO THIS AGREEMENT OR THE TRANSACTIONS CONTEMPLATED HEREBY IN ANY ACTION, PROCEEDING OR OTHER LITIGATION OF ANY TYPE BROUGHT BY ANY PARTY AGAINST ANY OTHER PARTY OR ANY AFFILIATE OF ANY OTHER SUCH PARTY, WHETHER WITH RESPECT TO CONTRACT CLAIMS, TORT CLAIMS OR OTHERWISE. THE PARTIES AGREE THAT ANY SUCH CLAIM OR CAUSE OF ACTION SHALL BE TRIED BY A COURT TRIAL WITHOUT A JURY. WITHOUT LIMITING THE FOREGOING, THE PARTIES FURTHER AGREE THAT THEIR RESPECTIVE RIGHT TO A TRIAL BY JURY IS WAIVED BY OPERATION OF THIS SECTION AS TO ANY ACTION, COUNTERCLAIM OR OTHER PROCEEDING WHICH SEEKS, IN WHOLE OR IN PART, TO CHALLENGE THE VALIDITY OR ENFORCEABILITY OF THIS AGREEMENT OR ANY PROVISION HEREOF. THIS WAIVER SHALL APPLY TO ANY SUBSEQUENT AMENDMENTS, RENEWALS, SUPPLEMENTS OR MODIFICATIONS TO THIS AGREEMENT.

(p) The parties agree that all disputes, legal actions, suits and proceedings arising out of or relating to this Agreement must be brought exclusively in the Court of Chancery of the State of Delaware (or, to the extent such court does not have subject matter jurisdiction, the Superior Court of the State of Delaware), or, if it has or can acquire jurisdiction, in the United States District Court for the District of Delaware (collectively the “Designated Courts”). Each party hereby consents and submits to the exclusive jurisdiction of the Designated Courts. No legal action, suit or proceeding with respect to this Agreement may be brought in any other forum. Each party hereby irrevocably waives all claims of immunity from jurisdiction, and any objection which such party may now or hereafter have to the laying of venue of any suit, action or proceeding in any Designated Court, including any right to object on the basis that any dispute, action, suit or proceeding brought in the Designated Courts has been brought in an improper or inconvenient forum or venue. Each of the parties also agrees that delivery of any process, summons, notice or document to a party hereof in compliance with Section 5(l) of this Agreement shall be effective service of process for any action, suit or proceeding in a Designated Court with respect to any matters to which the parties have submitted to jurisdiction as set forth above. Notwithstanding anything to the contrary herein, in no event will any party be liable for consequential, special, exemplary or punitive damages in connection with this Agreement or the transactions contemplated hereby.

(q) Nothing contained in this Agreement shall be deemed to vest in the Company or its subsidiaries any direct or indirect ownership or incidence of ownership of or with respect to the Holder’s Shares. All rights, ownership and economic benefits of and relating to the Holder’s Shares of the Holder shall remain fully vested in and belong to the Holder, and none of the Company or its subsidiaries shall have no authority to direct the Holder in the voting or disposition of any of the Holder’s Shares, except as otherwise provided herein.

(r) Holder hereby agrees that its representations, warranties and covenants set forth herein are solely for the benefit of the Company and its subsidiaries in accordance with and subject to the terms of this Agreement, and this Agreement is not intended to, and does not, confer upon any person other than the parties hereto any rights or remedies hereunder, including the right to rely upon the representations and warranties set forth herein, and the parties hereto hereby further agree that this Agreement may only be enforced against, and any action that may be based upon, arise out of or relate to this Agreement, or the negotiation, execution or performance of this Agreement may only be made against, the persons expressly named as parties hereto.

(s) If any provision of this Agreement is held invalid or unenforceable by any court of competent jurisdiction, the other provisions of this Agreement shall remain in full force and effect. The parties further agree that if any provision contained herein is, to any extent, held invalid or unenforceable in any respect under the laws governing this Agreement, they shall take any actions necessary to render the remaining provisions of this Agreement valid and enforceable to the fullest extent permitted by law and, to the extent necessary, shall amend or otherwise modify this Agreement to replace any provision contained herein that is held invalid or unenforceable with a valid and enforceable provision giving effect to the intent of the parties.

[Signature Page Follows]

IN WITNESS WHEREOF, the parties hereto have caused this Agreement to be executed as of the date first above written.