A two-sphere system with a two-lens zero-power corrector placed behind the secondary mirror was discussed. According to third-order aberration theory,the conditions of the absence of aberrations were analyzed,and the influences to the remaining high order aberrations of the system caused by the change of the relative aperture of the primary mirror,the position of the corrector and the different combination of the positive and negative lens in the corrector were investigated. The results show that the remaining aberrations will increase if the relative aperture of the primary increase or if the corrector approaches the secondary mirror. No matter the first lens of the corrector is positive or negative,there would be a particular optical power which causes smallest remaining aberrations,and it's better to use a negative lens near the secondary mirror.