POWER OF ATTORNEY

       With respect to holdings of and transactions in securities issued by
ContraFect Corporation (the "Company"), the undersigned hereby constitutes and
appoints the individuals named on Schedule A attached hereto and as may be
amended from time to time, or any of them signing singly, with full power of
substitution and resubstitution, to act as the undersigned's true and lawful
attorney-in-fact to:

       1.  prepare, execute in the undersigned's name and on the undersigned's
           behalf, and submit to the United States Securities and Exchange
           Commission (the "SEC") a Form ID, including amendments thereto, and
           any other documents necessary or appropriate to obtain and/or
           regenerate codes and passwords enabling the undersigned to make
           electronic filings with the SEC of reports required by Section 16(a)
           of the Securities Exchange Act of 1934, as amended, or any rule or
           regulation of the SEC;

       2.  execute for and on behalf of the undersigned, Forms 3, 4, and 5 in
           accordance with Section 16 of the Securities Exchange Act of 1934, as
           amended, and the rules thereunder;

       3.  do and perform any and all acts for and on behalf of the undersigned
           which may be necessary or desirable to complete and execute any such
           Form 3, 4, or 5, complete and execute any amendment or amendments
           thereto, and timely file such form with the SEC and any stock
           exchange or similar authority; and

       4.  take any other action of any type whatsoever in connection with the
           foregoing which, in the opinion of such attorney-in-fact, may be of
           benefit to, in the best interest of, or legally required by, the
           undersigned, it being understood that the documents executed by such
           attorney-in-fact on behalf of the undersigned pursuant to this Power
           of Attorney shall be in such form and shall contain such terms and
           conditions as such attorney-in-fact may approve in such attorney-in-
           fact's discretion.

       The undersigned hereby grants to each such attorney-in-fact full power
and authority to do and perform any and every act and thing whatsoever
requisite, necessary, or proper to be done in the exercise of any of the rights
and powers herein granted, as fully to all intents and purposes as the
undersigned might or could do if personally present, with full power of
substitution and resubstitution or revocation, hereby ratifying and confirming
all that such attorney-in-fact, or such attorneys-in-fact substitute or
substitutes, shall lawfully do or cause to be done by virtue of this Power of
Attorney and the rights and powers herein granted.

       The undersigned acknowledges that the foregoing attorneys-in-fact, in
serving in such capacity at the request of the undersigned, are not assuming,
nor is the Company assuming, any of the undersigned's responsibilities to comply
with Section 16 of the Securities Exchange Act of 1934, as amended.

       This Power of Attorney shall remain in full force and effect until the
undersigned is no longer required to file Forms 3, 4, and 5 with respect to the
undersigned's holdings of and transactions in securities issued by ContraFect
Corporation, unless earlier revoked by the undersigned in a signed writing
delivered to the foregoing attorneys-in-fact.

       IN WITNESS WHEREOF, the undersigned has caused this Power of Attorney to
be executed as of this 9th day of February 2021.


Signature:  /s/ Jane F. Barlow
            -----------------------------------
Print Name: Jane F. Barlow
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                                   Schedule A

Individuals Appointed as Attorney-in-Fact with Full Power of Substitution and
Resubstitution

Natalie Bogdanos
Michael Messinger