A secure S—box must exhibit the Strict Avalanche Criterion (SAC), ensuring that a single-bit change in the input causes each output bit to change with a probability close to 50%, thereby complicating differential and linear cryptanalysis. Despite its importance, analyses of deployed ciphers suggest that current S—box designs can still be improved. In this paper, we introduce a novel recursive method for constructing S—boxes that achieve perfect SAC by leveraging smaller S—boxes with SAC when combined with bitwise rotations. This approach systematically generates larger S—boxes while preserving and enhancing the cryptographic strengths of their smaller counterparts. The resulting S—boxes not only meet perfect SAC but also demonstrate competitive security properties and can be implemented using simple logic circuits, making them especially suitable for resource-constrained environments. Our findings contribute significantly to S—box design and offer substantial implications for developing robust cryptographic systems.