Schmidt system is a famous optical system. The corrector equation based on the third-order aberration theory has been acknowledged all along. When the previous equation is confirmed in characteristic of the aspheric surface equation and optical design program ZEMAX, it is found that the equation of the corrector has some errors. Analyses of this problem are given. A new corrector equation is established. The new equation is confirmed seriously by the optical design program ZEMAX again, it can be deduced that the coefficient a=1/2ra2, and the spherical aberration coefficient ∑S1=0. This improvement is very useful for the optical design of Schmidt system, which quickens the optimization and easily reaches the optimal design data.