In this paper, a fault detection problem is considered for a class of systems with unknown-but-bounded noises by a set-membership filtering approach. The measurement and the process noises are both considered as unknown-but-bounded. Two ellipsoidal sets, which are one-step-ahead prediction ellipsoid and estimation ellipsoid, are proposed for the state estimation. The fault signal is detected by intersecting the two ellipsoids to check whether the intersection set is empty or not. Recursive algorithms for calculating the two ellipsoids and for detecting whether the fault occurs in the system are developed. Simulation results are provided to illustrate the effectiveness of the proposed method.