It is well known that Schmidt system is a famous optical system. The equation of the corrector plate which was based on the third-order aberration theory was approved for a long time. When we confirmed the previous equation with optical design program ZEMAX,we found the coefficient of the equation a≠1/2r₀₂,where r₀₂ was the radius of the corrector plate vertex,and ΣS₁≠0,the focal length f and the back focal length f_b of Schmidt system also had some deviation,and didn't coincide with the third-order aberration theory. According to analysis,the cause of the errors was that the previous equation didn't contain the variation of the focal length after defocus Δ. The focal length after defocus should be f△=f+△.From the third-order aberration theory,substituting f with fΔ in calculation,we got a new equation of the corrector plate. Again,when we confirmed the new equation with optical design program ZEMAX,we could deduce that the coefficient a=1/2r₀₂,andΣS₁=0,which accorded with third-order aberration theory.