The basic functions in the method of moment (MoM) for 2D electromagnetic (EM) scattering problems that is symmetric about X-axis and Y-axis are obtained with the represention theory of finite group.We construct the group and get its regular representations.The tentative functions according to the four center symmetric positions are shown.While the regular representation is transformed into an irreducible one,orthonormal basic functions composed of the tentative functions are obtained.