The goal of this paper is to extend the fault detection procedure for MIMO system in order to isolate an anomaly once its presence detected, while insisting on the difficulties encountered within the framework of the set-membership approach. The proposed method is presented initially to deal with the case where only one fault may affect the system at a given moment then it is extended to the case of several faults while respecting a certain assumption. A fault can be either a parameter deviation (appearing in a multiplicative way in the model), or a bias affecting one of system outputs (appearing in an additive way). In both cases, a procedure of fault isolation is proposed in order to properly identify the failing component.