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Monitoring cluster evolution in data streams is a major research topic in data streams mining. Previous clustering methods for evolving data streams focus on global clustering result. It may lose critical information about individual cluster. This paper introduces some basic movements of evolution of an individual cluster. Based on the measurement of the movements, a novel algorithm called MovStream is proposed to monitor clusterspsila evolving in data streams. The experimental results on real datasets show that our MovStream algorithm surpasses the well-known CluStream algorithm by 25-50% in accuracy and one order of magnitude in efficiency.