EXHIBIT 10.13



                                 AMENDMENT NO. 5
                   TO AMTC CORPORATION STOCK OPTION AGREEMENT

         This Agreement is entered into as of March 1, 2003, between David P.
Cook ("Cook") and Zix Corporation, a Texas corporation ("ZixCorp"). Reference is
made to that certain AMTC Corporation Stock Option Agreement, effective as of
April 29, 1998, between Cook and ZixCorp (the "Cook Option").

1.       Amendments. The Cook Option is amended as follows:

         o    Revise Section 5 in its entirety to read as follows:

              "5. Expiration of Option. The Option shall expire, and shall not
              be exercisable thereafter with respect to any vested shares of
              Common Stock hereunder as to which the Option has not been
              exercised, on the sixth anniversary of the Award Date."

         o    Delete clause (c) and renumber existing clause (d) as clause (c)
              in Section 3.

2.       No Other Changes. Other than as provided herein, the Cook Option shall
         remain in full force and effect.


         Executed on the dates set forth below, to be effective as of the date
first set forth above.

                                     ZIX CORPORATION



                                     By:  /s/ Ronald A. Woessner
                                          -----------------------
                                          Ronald A. Woessner,
                                          Senior Vice President

                                     Date:   3-07-03
                                          -----------------------


                                     /s/ David P. Cook
                                     ----------------------------
                                     David P. Cook


                                     Date:   2/28/2003
                                          -----------------------


                                     /s/ Cheryl G. Cook
                                     ----------------------------
                                     Cheryl G. Cook


                                     Date:   2-28-03
                                          -----------------------