In this paper, we present a principled SVM based speaker verification system. A general approach to compute two sequences of frames is developed that enables the use of any kernel at the frame level. An extension of this approach using the Max operator is then proposed. The new system is compared to state-of-the-art GMM and other SVM based systems found in the literature on the Polyvar database. The new system outperforms, most of the time, the other systems, statistically significantly.