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In this paper, we present an algorithm to speed up the training of SVM. The proposed algorithm is based on SV candidates selection strategy, exploiting the observation that typically from a set of elements with the same label, if there exist SV, then most of them are on the boundary of the set. We compute the non convex hull sets that envelop the elements with the same label, this sets have in general a few elements compared with the entire data set. To train the SVM we use only the non convex hulls sets, which improves the training time. According to the results, our algorithm gives good accuracy and the training time is reduced considerably (under certain run conditions), the proposed algorithm is suitable for datasets with small number of features yet.