<PAGE>

                                                                     Exhibit 4.2


                              FIRST AMENDMENT TO
                          BOSTON LIFE SCIENCES, INC.
              WARRANTS FOR THE PURCHASE OF SHARES OF COMMON STOCK
                         NOS. BLSI - J-146 AND - J-147


     FIRST AMENDMENT TO WARRANTS (the "First Amendment") made and entered into
as of May 27, 2001, by and among Boston Life Sciences, Inc., a Delaware
corporation (the "Company"), and Pictet Global Sector-Fund Biotech (the
"Holder").

     REFERENCE is hereby made to the Boston Life Sciences, Inc. Warrant for the
Purchase of Shares of Common Stock Nos. BLSI - J-146 and - J-147 issued pursuant
to that certain Purchase Agreement among the Company and the Holder dated as of
May 26, 2000 (the "Warrants").

     WHEREAS, the Holder and the Company are in the process of negotiating in
good faith potential mutually beneficial amendments to the Warrants, which
negotiations have not yet concluded;

     WHEREAS, in consideration of and in order to provide additional time for
completion of such negotiations, the Holder and the Company desire to amend
certain time-sensitive provisions of each of the Warrants as set forth herein.

     NOW, THEREFORE, the parties to this Amendment agree as follows:

     1.   Amendment to Warrant No. BLSI - J-146.  The second sentence of the
          -------------------------------------
introductory paragraph of Warrant No. BLSI - J-146  (which sentence begins "If
the weighted average sales price per share") is hereby deleted and replaced in
its entirety with the following:

          "If the weighted average sales price per share of common stock of the
     company (as reported by Bloomberg Financial Services) for the 20 trading
     days ending on June 1, 2001 is less than $8.00 per share, then the exercise
     price of the warrant will be adjusted to the lower of (x) the weighted
                                                  --------
     average sales price per share of common stock of the company (as reported
     by Bloomberg Financial Services) for the 20 trading days ending on June 1,
     2001 and (y) the weighted average sales price per share of common stock of
     the company (as reported by Bloomberg Financial Services) for the 20
     trading days ending on June 15, 2001 (such lower price, the "Reset Price"),
     any such adjustment to be calculated and become effective as of June 16,
     2001."

     2.   Amendment to Warrant No. BLSI - J-147.  The second sentence of the
          -------------------------------------
introductory paragraph of Warrant No. BLSI - J-147  (which sentence begins "If
the weighted average sales price per share") is hereby deleted and replaced in
its entirety with the following:

          "If the weighted average sales price per share of common stock of the
     company (as reported by Bloomberg Financial Services) for the 20 trading
     days ending on June 1, 2001 is less than $10.00 per share, then the
     exercise price of the warrant will be adjusted to the lower of (x) the
                                                           --------
     weighted average sales price per share of common stock of the company (as
     reported by Bloomberg Financial Services) for the 20 trading days ending on
     June 1, 2001 and (y) the weighted average sales price per share of common
     stock of the company (as reported by
<PAGE>

     Bloomberg Financial Services) for the 20 trading days ending on June 15,
     2001 (such lower price, the "Reset Price"), any such adjustment to be
     calculated and become effective as of June 16, 2001."

     3.   Parties in Interest. All the terms and provisions of this First
          -------------------
Amendment shall be binding upon and inure to the benefit of and be enforceable
by the respective successors and permitted assigns of the parties hereto, and,
in particular, shall inure to the benefit of and be enforceable by any holder of
the Warrants, or its permitted assigns. This First Amendment shall be treated
for all purposes as having been incorporated into and become a part of each of
the Warrants and any party furnishing a copy of a Warrant to any person shall
furnish a copy of this First Amendment therewith.

     4.   Headings; Governing Law.  Sections 10 and 11 of the Warrants are
          -----------------------
incorporated herein by reference and shall govern this First Amendment in the
same manner as if set forth in its entirety herein.

     5.   Counterparts. This First Amendment may be executed concurrently in two
          ------------
or more counterparts, each of which shall be deemed an original, but all of
which together shall constitute one and the same instrument.

     6.   No Other Change. Except to the extent specifically amended hereby, the
          ---------------
provisions of the Warrants shall remain unmodified and the Warrants as amended
hereby are hereby confirmed as being in full force and effect.
<PAGE>

     IN WITNESS WHEREOF, the Company and the Holder have executed this First
Amendment as of the date and year first above written.




BOSTON LIFE SCIENCES, INC.


By: /s/ S. David Hillson
---------------------------------
Name:  S. David Hillson
Title:  Chairman, President and
Chief Executive Officer

PICTET GLOBAL SECTOR FUND-BIOTECH



By: /s/ Yves Martignier
---------------------------------
Name:  Yves Martignier
Title: Director