EXHIBIT 4.1
                       FIRST AMENDMENT TO RIGHTS AGREEMENT

         This First Amendment to Rights Agreement dated as of August 23, 1999
(this "AMENDMENT"), to the Preferred Shares Rights Agreement dated as of May
9, 1997 (the "AGREEMENT"), is entered into by and between General Surgical
Innovations, Inc., a California corporation (the "COMPANY"), and The U.S.
Stock Transfer Corporation (the "RIGHTS AGENT").

         Pursuant to Section 27 of the Agreement, this Amendment is being
executed by the Company and the Rights Agent for the purpose of amending the
Agreement as set forth below:

         The Agreement is hereby amended as follows:

         1.       Section 1(a) shall be amended by inserting the following at
                  the end of Section 1(a):

                  "Notwithstanding the foregoing or any provision to the
                  contrary in this Agreement, none of Tyco International Ltd., a
                  Bermuda corporation ("GUARANTOR"), General Acquisition Corp.,
                  a Nevada corporation and a direct, wholly-owned subsidiary of
                  Guarantor ("PARENT"), General Sub Acquisition Corp., a
                  California corporation and a direct, wholly-owned subsidiary
                  of Parent ("SUB"), or any of their respective subsidiaries,
                  Affiliates or Associates is an Acquiring Person pursuant to
                  this Agreement solely by virtue of the approval, execution or
                  delivery of the Agreement and Plan of Merger of even date
                  herewith among Parent, Sub and the Company (the "MERGER
                  AGREEMENT"), consummation of the transactions contemplated by
                  the Merger Agreement, including the Merger (as defined in the
                  Merger Agreement) or any public announcement of the
                  foregoing."

         2.       Section 1(h) shall be amended by inserting the following at
                  the end of Section 1(h):

                  "Notwithstanding the foregoing or any provision to the
                  contrary in this Agreement, a Distribution Date shall not
                  occur solely by virtue of the approval, execution or delivery
                  of the Merger Agreement, consummation of the transactions
                  contemplated by the Merger Agreement, including the Merger (as
                  defined in the Merger Agreement) or any public announcement of
                  the foregoing."

         3.       Section 1(t) shall be amended by inserting the following at
                  the end of Section 1(t):

                  "Notwithstanding the foregoing or any provision to the
                  contrary in this Agreement, a Section 13 Event shall not occur
                  solely by virtue of the approval, execution or delivery of the
                  Merger Agreement, consummation of the transactions
                  contemplated by the Merger Agreement, including the Merger (as
                  defined in the Merger Agreement) or any public announcement of
                  the foregoing."


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         4.       Section 1(u) shall be amended by inserting the following at
                  the end of Section 1(u):

                  "Notwithstanding the foregoing or any provision to the
                  contrary in this Agreement, a Shares Acquisition Date shall
                  not occur solely by virtue of the approval, execution or
                  delivery of the Merger Agreement, consummation of the
                  transactions contemplated by the Merger Agreement, including
                  the Merger (as defined in the Merger Agreement) or any public
                  announcement of the foregoing."

         5.       Section 1(y) shall be amended by inserting the following at
                  the end of Section 1(y):

                  "Notwithstanding the foregoing or any provision to the
                  contrary in this Agreement, a Triggering Event shall not occur
                  solely by virtue of the approval, execution or delivery of the
                  Merger Agreement, consummation of the transactions
                  contemplated by the Merger Agreement, including the Merger (as
                  defined in the Merger Agreement) or any public announcement of
                  the foregoing."

         6.       This Amendment shall be deemed to be entered into under the
                  laws of the State of California and for all purposes shall be
                  governed by and construed in accordance with the laws of such
                  State applicable to contracts to be made and performed
                  entirely within such State.

         7.       This Amendment may be executed in any number of counterparts
                  and each of such counterparts shall for all purposes be deemed
                  to be an original, and all such counterparts shall together
                  constitute but one and the same instrument.

         8.       As amended hereby, the Agreement shall remain in full force
                  and effect.

                            [SIGNATURE PAGE FOLLOWS]


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         The parties have duly executed this First Amendment to Rights
Agreement as of the day and year first written above.

                      THE "COMPANY"

                      GENERAL SURGICAL INNOVATIONS, INC.


                      By:      /s/ STEPHEN J. BONELLI
                               --------------------------------------------

                      Title:   Chief Financial Officer
                               --------------------------------------------
                               Vice President of Finance and Administration


                      Attest:    /s/ MARK B. WEEKS
                               --------------------------------------------



                      THE "RIGHTS AGENT"

                      THE U.S. STOCK TRANSFER CORPORATION


                      By:      /s/ WILLIAM GARZA
                               --------------------------------------------
                               Signature of Authorized Signatory

                      Title:   Assistant Vice President
                               --------------------------------------------