Using a support vector machine requires to set two types of hyperparameters: the soft margin parameter C and the parameters of the kernel. To perform this model selection task, one can use various procedures based on cross-validation. Obviously, the major drawback of such procedures rests in their time requirements. To overcome this difficulty, several upper bounds on the leave-one-out error of pattern recognition support vector machines have been derived. In this report, we demonstrate a direct extension of one of these bounds, called the radius-margin bound, to the case of the standard multi-class SVM.