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S-box is one of the most significant structures used to construct encryption that is strong and resistant to attacks in encryption algorithms. The new 4D-hyper chaotic system and deoxyribonucleic acid (DNA) computing are used in this paper to provide a new dynamic S-box generating approach. The 4D generated numbers are processed to generate a hexadecimal number that will encode using the DNA coding method and using addition, subtraction, and exclusive-or operations to produce the final DNA string decoded to make the S-Box. The dynamic form of s-boxes is represented by a minor change in the initial conditions of the proposed chaotic method that will generate dynamic sequences of numbers. The proposed method enhances the security criteria of the block ciphers. The S-box testing criteria were done like strict avalanche, balanced, and bit independence criteria, in addition to differential approximation probability and linearity approximation probability, to test the security of the new S-Box. The results show that the new S-box has good security and is resistant to attacks. [ABSTRACT FROM AUTHOR]