In this paper, we propose an approach for fast discovering all non-trivial repeating patterns in music objects. A repeating pattern is a sequence of notes which appears more than once in a music object. The longest repeating patterns in music objects are typically their themes. The themes and other non-trivial repeating patterns are important music features which can be used for both content-based retrieval of music data and music data analysis. We present a data structure called RT-tree and its associated algorithms for fast extracting all non-trivial repeating patterns in a music object. Experiments are performed to compare with the related approaches. The results are further analyzed to show the efficiency and the effectiveness of our approach.