Abstract. The present study investigates a geometrical method for optimizing the kernel function of a support vector machine. The method is an improvement of the one proposed in [4, 5]. It consists of using prior knowledge obtained from conventional SVM training to conformally rescale the initial kernel function, so that the separation between two classes of data is effectively enlarged. It turns out that the new algorithm works efficiently, has few free parameters, consumes very low computational cost, and overcomes the susceptibility of the original method.