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Real-time animation of human-like characters is an active research area in computer graphics. The conventional approaches have, however, hardly dealt with the rhythmic patterns of motions, which are essential in handling rhythmic motions such as dancing and locomotive motions. In this paper, we present a novel scheme for synthesizing a new motion from unlabelled example motions while preserving their rhythmic pattern. Our scheme first captures the motion beats from the example motions to extract the basic movements and their transitions. Based on those data, our scheme then constructs a movement transition graph that represents the example motions. Given an input sound signal, our scheme finally synthesizes a novel motion in an on-line manner while traversing the motion transition graph, which is synchronized with the input sound signal and also satisfies kinematic constraints given explicitly and implicitly. Through experiments, we have demonstrated that our scheme can effectively produce a variety of rhythmic motions.