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Support vector machine (SVM) is not suitable for classification on large data sets due to its training complexity. Convex hull can simplify SVM training, however the classification accuracy becomes lower when there are inseparable points. This paper introduces a novel method for SVM classification, called convex-concave hull. After a grid processing, the convex hull is used to find extreme points. Then we detect a concave (non-convex) hull, the vertices of it are used to train SVM. We applied the proposed method on several problems. Experimental results demonstrate that our approach has good classification accuracy while the training is significantly faster than other state of the art methods.