Hudson Executive Investment Corp III (HIII) S-1IPO registration

Exhibit 4.1

UNITS

NUMBER

U-

SEE REVERSE FOR CERTAIN DEFINITIONS

CUSIP

HUDSON EXECUTIVE INVESTMENT CORP. III

UNITS CONSISTING OF ONE SHARE OF CLASS A COMMON STOCK AND ONE-FIFTH OF ONE

REDEEMABLE WARRANT, EACH WHOLE WARRANT ENTITLING THE HOLDER TO PURCHASE

ONE SHARE OF CLASS A COMMON STOCK

THIS CERTIFIES THAT is the owner of Units.

Each Unit (“Unit”) consists of one share of Class A common stock, par value $0.0001 per share (“Common Stock”), of Hudson Executive Investment Corp. III, a Delaware corporation (the “Company”), and one-fifth of one redeemable warrant (the “Warrant”). Each whole Warrant entitles the holder to purchase one share of Common Stock for $11.50 per share (subject to adjustment). Only whole Warrants are exercisable. Each whole Warrant will become exercisable on the later of (i) thirty (30) days after the Company’s completion of a merger, capital stock exchange, asset acquisition, stock purchase, reorganization or other similar business combination with one or more businesses (each a “Business Combination”), and (ii) twelve (12) months from the closing of the Company’s initial public offering, and will expire unless exercised before 5:00 p.m., New York City Time, on the date that is five (5) years after the date on which the Company completes its initial Business Combination, or earlier upon redemption or liquidation (the “Expiration Date”). The Common Stock and Warrants comprising the Units represented by this certificate are not transferable separately prior to [ ], unless [•] and [•] elect to allow separate trading earlier, subject to the Company’s filing of a Current Report on Form 8-K with the Securities and Exchange Commission containing an audited balance sheet reflecting the Company’s receipt of the gross proceeds of the Company’s initial public offering and issuing a press release announcing when separate trading will begin. No fractional Warrants will be issued upon separation of the Units. The terms of the Warrants are governed by a Warrant Agreement, dated as of [ ], between the Company and Continental Stock Transfer & Trust Company, as Warrant Agent, and are subject to the terms and provisions contained therein, all of which terms and provisions the holder of this certificate consents to by acceptance hereof. Copies of the Warrant Agreement are on file at the office of the Warrant Agent at 1 State Street, 30th Floor, New York, New York 10004, and are available to any Warrant holder on written request and without cost.

This certificate is not valid unless countersigned by the Transfer Agent and registered by the Registrar of the Company.

This certificate shall be governed by and construed in accordance with the internal laws of the State of New York.

Witness the facsimile signature of a duly authorized signatory of the Company.

Hudson Executive Investment Corp. III

The Company will furnish without charge to each unitholder who so requests, a statement of the powers, designations, preferences and relative, participating, optional or other special rights of each class of equity or series thereof of the Company and the qualifications, limitations, or restrictions of such preferences and/or rights.

The following abbreviations, when used in the inscription on the face of this certificate, shall be construed as though they were written out in full according to applicable laws or regulations:

Additional abbreviations may also be used though not in the above list.

For value received, hereby sell, assign and transfer unto

(PLEASE INSERT SOCIAL SECURITY OR OTHER IDENTIFYING NUMBER OF ASSIGNEE)

(PLEASE PRINT OR TYPEWRITE NAME AND ADDRESS, INCLUDING ZIP CODE, OF ASSIGNEE)

Units represented by the within Certificate, and do hereby irrevocably constitute and appoint

Attorney to transfer the said Units on the books of the within named Company with full power of substitution in the premises.

As more fully described in, and subject to the terms and conditions described in, the Company’s final prospectus for its initial public offering dated [    ], the holder(s) of this certificate shall be entitled to receive a pro rata portion of certain funds held in the trust account established in connection with the Company’s initial public offering only in the event that (i) the Company redeems the shares of Common Stock sold in the Company’s initial public offering and liquidates because it does not consummate an initial business combination by the date set forth (the “Last Date”) in the Company’s Amended and Restated Certificate of Incorporation, as the same may be amended from time to time (the “Charter”), (ii) the Company redeems the shares of Common Stock sold in its initial public offering properly submitted in connection with a stockholder vote to amend the Charter to modify the substance or timing of the Company’s obligation to redeem 100% of the Common Stock if it does not consummate an initial business combination by the Last Date or with respect to any other material provisions relating to stockholders’ rights or pre-initial business combination activity, or (iii) if the holder(s) seek(s) to redeem for cash his, her or its respective shares of Common Stock in connection with a tender offer (or proxy solicitation, solely in the event the Company seeks stockholder approval of the proposed initial business combination) setting forth the details of a proposed initial business combination. In no other circumstances shall the holder(s) have any right or interest of any kind in or to the trust account.