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In this paper, we propose a novel approach that looks for the most discriminating points in horizontal, vertical, velocity and pressure trajectories. Then based on these discriminating points, we have made two composite feature sets i.e. (horizontal; vertical) and (velocity; pressure). Out of these two composite feature sets, one will be declared as the most discriminating composite feature set during the training phase. Finally the verification based on the selected discriminating composite feature will be performed. We believe that every signer has some discriminating points that a forger cannot mimic with certain pressure and velocity whereas these points are maintained by the genuine signer. So the verification based on these discriminating points can lead us to a better performance of the verification system. For a reliable verification system, comparison between forgery and genuine signer should be made on the basis of discriminating points rather than using all the sample points of each trajectory in the verification which means that all the points are given equal weights and there is always a possibility that the non-discriminating points can overshadow the effect of discriminating points. Experimental results demonstrate superiority of our approach in On-line signature verification in comparison with other techniques.