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The pseudospectral time-domain (PSTD) method has shown a marked improvement in accuracy and efficiency over the FDTD method. Nevertheless, it likewise suffers from the CFL stability condition. In this work, based on the concepts of ADI- and SS-FDTD methods, as well as our previously developed 3D PSTD method (G. Zhao et al, IEEE Microwave Wireless Compon. Lett.), we derive the unconditionally stable multidomain PSTD algorithm. We demonstrate that the implicit finite difference scheme can be applied to the PSTD method and make it free of the CFL stability condition.