This note deals with the exact Fault Detection and Isolation problem. In the case of observer-based residual generation, the problem amounts to find two gain matrices such that the two problems are simultaneously solved. It is known that the freedom in eigenstructure assignment leads to well-conditioned design which is robust to unstructured uncertainties. The approach here considered aims to design a residual generator trough a full-order observer to achieve fault detection and isolation by means of right and left eigenstructure assignment. Moreover when diagonal isolation cannot be obtained, an almost isolation method, based on a functional minimization, is proposed. A numerical example shows the effectiveness of the contribution here presented.