The dispersion in a chirped pulse amplifier (CPA) with a Martinez stretcher is analyzed theoretically based on ray_tracing. The method of mutual compensation th at introduced properly the negative third_order dispersion to balance the fifth_ order dispersion is presented. A shorter pulse near the transform_limit can be g enerated by this method rather than by the traditional approach that zeros the s econd and the third order dispersion successively in the CPA system.