The Parity Space Approach (PSA) in time domain and the H² approach in frequency domain are two important approaches to design robust Fault Detection (FD) systems. Compared with the H² approach, the PSA is simpler in design but has a poorer performance index unless it adopts a parity vector of a very high order, which will lead to an unacceptable computational load. In this paper, a new approach to design a PSA based FD system in frequency domain is proposed, in which the optimal performance index of the H² approach can be realized with a low order PSA based residual generator and a simple narrowband filter. The new approach ensures a simple design form similar to that of the PSA, an optimal performance index as good as that of the H² approach, a low computational load and an easy online realization simultaneously. Keywords. Fault detection, H², optimization, parity space approach, robustness