We introduce a generalization to the multiclass framework of a previous approach to Boosting by constructing symmetric functions. This approach contrasts with the usual ADABOOST-type Boosting algorithms using linear separators. Indeed, multiclass induction does not necessitate combination tricks such as those for linear separators, and it achieves some novel agnostic learning properties, as well as significant malicious noise tolerance. Experiments on a large testbed against ADABOOST and C4.5 display the efficiency of the approach proned.