S-boxes are the only nonlinear component in many algorithms for encryption, int ension of which decides the security strength of the whole algorithm. By theoret ical analysis and statistics, there is evidence showing that large S-boxes hav e better cryptographic properties than small S-boxes. But they are harder to de sign and to implement. Now the 8×8 S-box is popular. In this paper, a method f or constructing the 8×8 S-box and 8×6 S-box based on m-sequence is describe d. Through testing, some S-boxes with better nonlinearity and better difference uniformity are obtained. Finally some 4×4 S-boxes based on orthomorphic permu tation are designed. These S-boxes offer the nonlinear resouce for further desi gn of cryptographic algorithms.