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In this paper, we propose a new directional analysis tool for On-line signatures that decomposes the given input signature into directional bands on the basis of relative angles. Our directional analysis tool takes the independent trajectories (horizontal and vertical) as an input and then decomposes them into directional bands on the basis of relative angles. We have used both user-dependent and user-independent thresholds for selecting an optimal number of partitions for each signer. By decomposing signature trajectories based upon relative angles of an individualpsilas signature, the resulting process can be thought of as one that exploits inter-feature dependencies . In the verification phase, distances of each partitioned trajectory of a test signature are calculated against a similarly partitioned template trajectory for a known signer. Each partition is then weighted based on its quality and quantity. Experimental results demonstrate the superiority of our approach to On-line signature verification in comparison with other techniques.