Constellation Alpha Capital Corp. Emerald View, Suite 400, 2054 Vista Parkway West Palm Beach, FL 33411

Exhibit 10.4

Constellation Alpha Capital Corp.

Emerald View, Suite 400, 2054 Vista Parkway

West Palm Beach, FL 33411

June 19, 2017

Centripetal, LLC

Emerald View, Suite 400, 2054 Vista Parkway

West Palm Beach, FL 33411

Ladies and Gentlemen:

This letter agreement will confirm our agreement that, commencing on the first date (the “Effective Date”) that any securities of Constellation Alpha Capital Corp. (the “Company”) registered on the Company’s registration statement (the “Registration Statement”) for its initial public offering (the “IPO”) are listed on the Nasdaq Capital Market, and continuing until the earlier of (i) the consummation by the Company of an initial business combination and (ii) the Company’s liquidation (in each case as described in the Registration Statement) (such earlier date hereinafter referred to as the “Termination Date”), Centripetal, LLC shall make available to the Company certain office space, utilities and secretarial and administrative services as may be required by the Company from time to time, situated at Emerald View, Suite 400, 2054 Vista Parkway, West Palm Beach, FL 33411 (or any successor location). In exchange therefor, the Company shall pay Centripetal, LLC the sum of $10,000 per month on the Effective Date and continuing monthly thereafter until the Termination Date. Centripetal, LLC hereby agrees that it does not have any right, title, interest or claim of any kind in or to any monies that may be set aside in a trust account (the “Trust Account”) that may be established upon the consummation of the IPO as a result of this letter agreement (the “Claim”) and hereby irrevocably waives any Claim it may have in the future as a result of, or arising out of, this letter agreement and will not seek recourse against the Trust Account for any reason whatsoever.

This letter agreement constitutes the entire agreement and understanding of the parties hereto in respect of its subject matter and supersedes all prior understandings, agreements, or representations by or among the parties hereto, written or oral, to the extent they relate in any way to the subject matter hereof or the transactions contemplated hereby.

This letter agreement may not be amended, modified or waived as to any particular provision, except by a written instrument executed by all parties hereto.

No party hereto may assign either this letter agreement or any of its rights, interests, or obligations hereunder without the prior written approval of the other party. Any purported assignment in violation of this paragraph shall be void and ineffectual and shall not operate to transfer or assign any interest or title to the purported assignee.

Any litigation between the parties (whether grounded in contract, tort, statute, law or equity) shall be governed by, construed in accordance with, and interpreted pursuant to the laws of the State of New York, without giving effect to its choice of laws principles.

AGREED TO AND ACCEPTED BY: