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                                                                     EXHIBIT 4.1

                       FIRST AMENDMENT TO RIGHTS AGREEMENT

     This First Amendment to Rights Agreement dated as of October 3, 2000 (this
"AMENDMENT"), to the Preferred Shares Rights Agreement dated as of September 19,
1997 (the "AGREEMENT"), is entered into by and between InnerDyne, Inc., a
Delaware corporation (the "COMPANY"), and American Stock Transfer and Trust
Company (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 company
          ("GUARANTOR"), Tyco Acquisition Corp. X, a Delaware corporation and a
          direct, wholly-owned subsidiary of Guarantor ("PARENT"), VLMS, Inc., a
          Delaware 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 Offer and 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 Offer and 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

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          Agreement, including the Offer and the Merger (as defined in the
          Merger Agreement) or any public announcement of the foregoing."

     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 Offer and 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 Offer and 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 New York 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"

                                       INNERDYNE, INC.


                                       By:
                                          --------------------------------------
                                          Name:
                                          Title:




                                      THE "RIGHTS AGENT"

                                      AMERICAN STOCK TRANSFER
                                        AND TRUST COMPANY


                                       By:
                                          --------------------------------------
                                               Authorized Signatory