CSKH.01.2018 - (Abstract)— This paper presents an algorithm for evaluating the linear redundancy and the factor of inertial groups with small computational complexity. Specifically, the article introduces the concept of the factor of inertial groups, the relationship between the factor of inertial groups and the linear redundancy of S-box. Thus, it is recommended to use S-boxes that do not possess linear redundancy and have the factor of inertial groups equal to 1 to have better cryptographic properties, and also provide an algorithm for searching such large size S-boxes.