Abstract: Determining the number of clusters is one of the most important topic in cluster analysis. The ability of clustering algorithm to distinguish between overlapping clusters is one of the major criteria for evaluating its efficiency. However, cluster overlapping phenomenon is not yet well understood by researchers. This study, a definition was presented on the degree of overlap between two clusters firstly. Based on this definition, an algorithm was developed for calculating the overlap rate. Then it was show that how the theory can be used to deal with the problem of cluster merging in a hierarchical approach to clustering and gave an optimal number of clusters automatically. Furthermore, comparison was made between the proposed new method and the previous related works. Finally, the experimental results demonstrate the effectiveness of the overlap rate measuring method and the new hierarchical clustering algorithm.