To set the values of the hyperparameters of a support vector machine (SVM), one can use cross-validation. Its leave-one-out variant produces an estimator of the generalization error which is almost unbiased. Its major drawback rests in its time requirement. To overcome this difficulty, several upper bounds on the leave-one-out error of the pattern recognition SVM have been derived. The most popular one is the radius-margin bound. In this article, we introduce a generalized radius-margin bound dedicated to the multi-class SVM of Lee, Lin and Wahba.