In this paper. we develop a design method of an unknown input observer(UIO) for system with unknown inputs present in the state and output equations. The proposed design method makes use of estimates of unknown inputs. This method has an advantage that all additive unknown inputs can be dealt with by a consistent approach. And two conditions are derived, which are sufficient conditions for a stable UIO to be. The conditions can be tested by given system matrices. Finally. a simulation is performed to verify developments in this paper. We study fault diagnosis of flight control system in the simulation.