Exhibit 24

                            LIMITED POWER OF ATTORNEY

                            LIMITED POWER OF ATTORNEY

        The undersigned hereby constitutes and appoints Martin W. Mackay,
Jeffrey M. Fryer and Michael Greco, with full power of substitution, 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 U.S. Securities and
               Exchange Commission (the "SEC") a Form ID, including amendments
               thereto, and any other documents necessary or appropriate to
               obtain 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, in the
               undersigned's capacity as officer and/or director of Rallybio
               Corporation (the "Company"), Forms 3, 4, 5 and any Schedules 13D
               or 13G in accordance with Section 16(a) 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 that may be necessary or desirable to complete and
               execute any such Form 3, 4, or 5 or Schedule 13D or 13G,
               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 that, in the opinion of each 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 each 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 each
               such attorney-in-fact may approve in each 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 or revocation, hereby ratifying and confirming all that each such
attorney-in-fact, or each such attorney-in-fact's 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 each
foregoing attorney-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, 5, and any Schedules 13D
or 13G with respect to the undersigned's holdings of and transactions in
securities issued by the Company, unless earlier revoked by the undersigned in
a signed writing delivered to each foregoing attorney-in-fact.

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        IN WITNESS WHEREOF, the undersigned has caused this Power of Attorney
to be executed as of this 31st day of March, 2022.

                                   /s/ Christine A. Nash
                                   -------------------------------
                                   Name: Christine A. Nash