In this work state estimation for unknown input discrete-time linear systems is tackled in a bounded error context. First, under the boundedness assumption on both process and measurement noise as well as on system’s initial state, the estimation problem is reformulated as a reachability problem. Then, by preprocessing the set-valued expression of the general solution of the state equation and applying zonotopic set computation rules, a non-conservative and computationally tractable algorithm is proposed to characterize efficiently the solution set of this problem. Numerical examples are presented to show the performance of the proposed zonotopic unknown input state estimator.