The paper deals with the problem of designing observers for a class of discrete-time nonlinear systems with an unknown input. In particular, with the use of the Lyapunov method, a design procedure of an asymptotically convergent observer is proposed. Moreover, the e ect of decoupling an unknown input is investigated in the light of an undesirable decoupling of possible faults. As a result, a condition for checking an undesirable fault decoupling is provided. Subsequently, it is shown how to employ the proposed robust fault diagnosis observer for the non-linear systems with state constraints. The final part of the paper shows experimental results that confirm the e ectiveness of the proposed approach and the potential profits that can be achieved while applying the proposed approach in the fault diagnosis scheme.