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Based on in-depth study of rough set theory, an equivalent algorithm for computing positive region is proposed and the algorithm divides information system into position region and non-position region. Then, an algorithm for fast computing positive region in incremental condition attribute system is proposed by analysing influence of increased condition attribute to the set of known positive region. The algorithm computes positive region on the basic of originally positive region and improves the computing speed. The theoretical analysis and experimental results show the new algorithm is much more efficient and useful in computing.