Abstract: By using the secondorder moments method and generalized HuygensFresnel diffraction integral, the optical system used for symmetrizing Hermite Gaussian beams with real argument is applied to study the transformation of astigmatic HermiteGaussian beams with complex argument. It is shown that the secondorder matrix of HermiteGaussian beams with complex argument passing through this system can be symmetrized．However， the spot shape of the beams has not a rotational symmetry . Therefore, such type of symmetrization system for beams with real argument is not suitable for beams with complex argument.