In a DES-like cryptosystem, the S(ubstitution) boxes determine its cryptographic strength as well as its nonlinearity. When in an S box a part of the output depends on a part of the input. It can be broken by the chosen plaintext attack. To prevent this attack, every output bit should changes with a probability of one half when ever a single input bit is complemented. We call this criterion Strict Avalanche criterion(SAC), which was proposed by Webster and Tavared. In this paper, we propose simple construction method of Boolean functions satisfying the SAC and bijective functions satisfying the maximum order SAC in order to design cryptographically desirable S-boxes. Also, practical construction examples of S-boxes are provided.