Product codes are a type of error-correcting code that provide excellent error correction performance due to their large minimum Hamming distance. However, they suffer from high decoding complexity. This paper proposes a new decoding algorithm that utilizes information from the dual codes of the component codes, incorporating a priori probability values into the component decoding process. This approach eliminates the assumption of equal probability for code bits, leading to improved decoding performance. The algorithm was simulated for Hamming codes (7, 4), (15, 11), and (31, 26). The simulation results demonstrate that the BER reaches \({10}^{-6}\) at an SNR of 3.87 dB for a product code with Hamming (31, 26) components. Furthermore, the proposed algorithm offers a decoding gain of 0.3 dB and reduces complexity (with a linear function of \(O\left(n.{2}^{r}\right)\) ) by 56% compared to the Maximum A Posteriori Probability algorithm for the same type of product code.