The purpose of this article is to present a new procedure for industrial process diagnosis. This method is based on bayesian classifiers. A feature selection is done before the classification between the different faults of a process. The feature selection is based on a new result about mutual information that we demonstrate. The performances of this method are evaluated on the data of a benchmark example: the Tennessee Eastman Process. Three kinds of fault are taken into account on this complex process. The challenging objective is to obtain the minimal recognition error rate for these 3 faults. Results are given and compared on the same data with those of other published methods