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The Advanced Encryption Standard (AES) is widely used in different kinds of security applications. The substitution box (S-box) is the main component of many modern symmetric encryption ciphers that provides confusion between the secret key and ciphertext. The S-box component that is used in AES is fixed. If we construct this component dynamically, the encryption strength of AES would be greater than before. In this manuscript, we used chaotic logistic map, Mobius transformation and symmetric group S 256 to construct S-box for AES. The idea behind the proposed work is to make supplementary safe S-box. The presented S-box is analyzed for the following analyses: linear approximation probability (LP), nonlinearity (NL), differential approximation probability (DP), strict avalanche criterion (SAC), and bit independence criterion (BIC). The analyses show that the proposed technique is useful in generating high resistance S-box to known attacks.