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The problem of extending binary support vector machines (SVMs) for multiclass classification is still an ongoing research issue. Ussivakul and Kijsirikul proposed the Adaptive Directed Acyclic Graph (ADAG) approach that provides accuracy comparable to that of the standard algorithm-Max Wins and requires low computation. However, different sequences of nodes in the ADAG may provide different accuracy. In this paper we present a new method for multiclass classification, Reordering ADAG, which is the modification of the original ADAG method. We show examples to exemplify that the margin (or 2/|w| value) between two classes of each binary SVM classifier affects the accuracy of classification, and this margin indicates the magnitude of confusion between the two classes. In this paper, we propose an algorithm to choose an optimal sequence of nodes in the ADAG by considering the |w| values of all classifiers to be used in data classification. We then compare our performance with previous methods including the ADAG and the Max Wins algorithm. Experimental results demonstrate that our method gives higher accuracy. Moreover it runs faster than Max Wins, especially when the number of classes and/or the number of dimensions are relatively large.