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                                                                    EXHIBIT 10.1

                             ARCH CAPITAL GROUP LTD.

                     AMENDMENT TO RESTRICTED SHARE AGREEMENT

     WHEREAS, Arch Capital Group Ltd. (the "COMPANY"), a Bermuda company,
awarded 1,668,157 restricted common shares to Robert Clements (the "EXECUTIVE")
pursuant to a restricted share agreement, dated October 23, 2001, between the
Company and the Executive (the "AGREEMENT"); and capitalized terms used without
definition herein have the meanings given to them in the Agreement;

     NOW, THEREFORE, in consideration of the premises and mutual covenants
contained herein, the parties have agreed to amend the Agreement as follows:

     1.   The first sentence of Section 2(a) shall be amended and restated in
          its entirety as follows:

          "Subject to Section 2(b) below and the other terms and conditions of
          this Agreement, this Award shall become vested in three installments
          as follows: (i) 1,000,894 common shares, par value $0.01 per share
          ("COMMON SHARES"), of the Company (i.e., 60% of the shares subject to
          the Award) shall vest on October 23, 2002 and (ii) 667,263 Common
          Shares shall vest in two equal annual installments, commencing on
          October 23, 2003."

     2.   All other provisions of the Agreement shall remain in full force and
effect. This amendment shall be governed by and construed in accordance with the
laws of Bermuda, without giving effect to principles of conflict of laws, and
may be executed in two counterparts, each of which shall constitute one and the
same instrument.

     IN WITNESS WHEREOF, the undersigned have executed this agreement as of
October 23, 2002.

                                   ARCH CAPITAL GROUP LTD.


                                   By: /s/ John D. Vollaro
                                      -----------------------------------
                                      Name: John D. Vollaro
                                      Title: Executive Vice President and Chief
                                      Financial Officer


                                     /s/ Robert Clements
                                     ---------------------------------------
                                     Robert Clements