The neural networks are successfully applied to many applications in different domains. However, due to the results made by the neural networks are difficult to explain the decision process of neural networks is supposed as a black box. The explanation of reasoning is important to some applications such like credit approval application and medical diagnosing software. Therefore, the rule extraction algorithm is becoming more and more important in explaining the extracted rules from the neural networks. In this paper, a decompositional algorithm is analyzed and designed to extract rules from neural networks. The algorithm is simple but efficient; can reduce the extracted rules but improve the efficiency of the algorithm at the same time. Moreover, the algorithm is compared to the other two algorithms, M-of-N and Garcez, by solving the MONK's problem.