1 AGREEMENT APPOINTING A SUCCESSOR Exhibit 4.1 RIGHTS AGENT UNDER RIGHTS AGREEMENT AGREEMENT, dated as of June 1, 1999, among Service Corporation International, a Texas corporation (the "Company"), Harris Trust and Savings Bank ("Harris Trust") and The Bank of New York ("BNY"). The Company and Harris Trust have heretofore executed and entered into the Rights Agreement, dated as of May 14, 1998 (the "Rights Agreement"), under which Harris Trust is the Rights Agent. Pursuant to Section 21 of the Rights Agreement, the Company may appoint a successor to the Rights Agent in accordance with the provisions of Section 21 thereof. All acts and things necessary to make this Agreement a valid agreement, enforceable according to its terms, have been done and performed, and the execution and delivery of this Agreement by the undersigned have been in all respects duly authorized by the undersigned. In consideration of the foregoing and the mutual agreements set forth herein, the parties hereto agree as follows: 1. Effective as of June 1, 1999, Harris Trust resigns as Rights Agent under the Rights Agreement and the Company appoints BNY as the Rights Agent under the Rights Agreement. 2. Harris Trust and the Company each hereby waive any notice required by Section 21 of the Rights Agreement. 3. BNY represents that it, together with its Texas subsidiaries and affiliates, meets the requirements to be Rights Agent as set forth in Section 21 of the Rights Agreement. BNY accepts its appointment as Rights Agent under the Rights Agreement and agrees to act as Rights Agent in accordance with the terms of the Rights Agreement. IN WITNESS WHEREOF, the parties hereto have caused this Agreement to be duly executed and attested, all as of the date and year first above written. Attest: SERVICE CORPORATION INTERNATIONAL By: /s/ Curtis G. Briggs By: /s/ James M. Shelger ----------------------------------- --------------------------------------------- Senior Vice President Attest: HARRIS TRUST AND SAVINGS BANK By: /s/ Lorraine Rodewald By: /s/ Ray G. Rosenbaum ------------------------------------ ---------------------------------------------- Vice President Attest: THE BANK OF NEW YORK By: /s/ Steven R. Myers By: /s/ James Dimino ------------------------------------ ----------------------------------------------