This study deals with the problem of fault detection (FD) for linear discrete time-varying (LDTV) systems by combining the parity space-based method with the stationary wavelet transform (SWT). For the purpose of achieving good FD performance and simultaneously reducing the online computational burden resulted by high parity space order, SWT on residual signal is the first step in this study. This allows the formulation of residual generation as the selection of wavelet basis for SWT and the design of time-varying parity space vectors in a framework of multiscale optimisation. A recursive algorithm is developed for the computation of optimal parity space vectors and, based on this, a bank of residual signals can be obtained. Moreover, a weighted multiscale residual evaluation strategy is presented to detect the occurrence of a fault. The major contribution of the study lies in the development of a recursive design of SWT aided parity space vectors, which delivers an improvement of FD performance for a lower parity space order and an easy online implementation. A numerical example is demonstrated to illustrate the effectiveness of the proposed method.