The aim of the paper is to report a new method based on genetic computation of designing a nonlinear soft margin SVM yielding to significant improvements in discriminating between two classes. The design of the SVM is performed in a supervised way, in general the samples coming from the classes being nonlinearly separable. The experimental analysis was performed on artificially generated data as well as on Ripley and MONK's datasets reported in the fourth section of the paper. The tests proved real improvements of both the recognition rate and generalization capacities without significantly increasing the computational complexity.