In this paper, an iterative residual generator (IRG) is proposed for discrete time-invariant state-space model with the aim of detecting faulty signals. By minimizing the mean square errors subject to unbiasedness constraint, a new filter with finite impulse response structure is derived. The resulting IRG is then obtained by extracting residual signal from the batch filter through several predictor/corrector iterations. It shows that IRG can provide a zero-mean Gaussian process regardless of previous estimation errors. More importantly, it includes the residual generation process in the Kalman filter as its special case. With the chi-square test, a numerical example is simulated to demonstrate that IRG can reduce the false alarm significantly compared with the traditional recursive strategy in the presence of actuator or sensor faults, and the estimation horizon length in IRG serves as a tuning parameter providing a tradeoff between the missed alarm and false alarm.