In recent years, the music has become popular due to the evolution of the technology. Various kinds of music around us become complexities and huge. The explosive growth in the music has generated the urgent need for new techniques and tools that can intelligently and automatically transform the music into useful information. Many researches consider the music object as an continuously discrete note in time order. Repeating patterns are some subsequences which appear frequently in the music sequence. The repeating patterns usually can represent the theme of a music object. Moreover, it also can be utilized in music classification. Many methods have been proposed for finding the repeating patterns in music objects, for example, the M2P (Mining Maximum-length Patterns) method. It constructs a directed graph and uses the depth-first search to traverse the graph. It calculates the paths by the string matching algorithm to decide whether they are repeating pattern, and finds out the maximum-length repeating pattern in a music sequence. Although the M2P method is a straightforward method to find out the patterns, it consumes time in creating too many candidate patterns and performing the string matching algorithm. Therefore, in this thesis, we propose the PJ (Position-Join) method to efficiently find out the maximum-length repeating pattern. In the constructing graph step, we find out that we can modify the information in the graph, and avoid to use the string matching algorithm to decide whether a path is repeating pattern. We record the positions of length two repeating patterns in the matrix. While traversing the graph, we calculate the frequency by the information of positions. Moreover, we record the repeated path by the positions. We create terminal edges, and record the information of paths which have been traversed. We dynamically modify the graph by terminal edges. It can avoid to traverse some paths repeatedly in traversing the graph step. From our performance study based on the synthetic data and real music data, we show that our proposed PJ method is more efficient than the M2P method.