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In this paper, we propose a method of online signature verification system using HMM models in a polar coordinate system. In the previous works, the signature verification was performed in terms of a standard X-Y coordinate system. This coordinate system always needs the normalization of signature stroke size and angle variance. To reduce normalization error and computing time, we propose the polar coordinate system. Under the polar coordinate system, the feature sets are robust and independent of size and angle variation according to the user characteristics. The use of HMMs instead of a traditional Euclidian distance metric for the determination of the degree of match between a test signature and a reference signature model brings about a significant improvement in performance as it permits the incorporation of heuristics. The experiments shows that the proposed method gives lower equal error rate 2.2% from 50,000 testing cases.