A fault detection method applied to a redundant strapdown inertial navigation system, which usually undergoes rapid maneuvers, is developed in this paper. First, an improved four-points detection scheme that can significantly reduce the probability of false alarm of the generalized likelihood test(GLT) is present. Then, based on analyzing influences on the fault detection performance caused by the misalignment and scale fator errors and the random bias of a gyroscope, a parity vector error model is constructed and sequently the Kalman filtering scheme to compensate the parity vector error is designed. By example of a redundant measurement unit with four single-freedom-degree gyros, the fault detection method has been analyzed qualitatively and quantitatively through simulation tests. Simulation results demonstrate the favorable performance of the method.