This paper deals with the problem of the optimal fault detection(FD) for linear discrete time-varying(LDTV) systems with delayed state and l2-norm bounded unknown input. The novelty lies in the designing of an evaluation function for the robust FD. The basic idea is to directly construct an evaluation function by using a weighted l2-norm of the measurement output, which achieves an optimal trade-off between the sensitivity to fault and the robustness to l2-norm bounded unknown input. To avoid complex computation, a feasible solution is obtained via the recursive computation by applying the orthogonal projection. It is shown that such an evaluation function provides a unified scheme for both the cases of unknown input being l2-norm bounded and jointly normal distribution, while a threshold may be chosen based on a priori knowledge of unknown input. A numerical example is given to demonstrate the effectiveness of the proposed method. This paper deals with the problem of the optimal fault detection (FD) for linear discrete time-varying (LDTV) systems with delayed state and l2-norm bounded unknown input. The novelty lies in the designing of an evaluation function for the robust FD. The basic idea is to directly construct an evaluation function by using a weighted l2-norm of the measurement output, which achieves an optimal trade-off between the sensitivity to fault and the robustness to l2-norm bounded unknown input. To avoid complex computation, a feasible solution is obtained via the recursive computation by applying the orthogonal projection. It is shown that such an an evaluation function provides a unified scheme for both the cases of unknown input being l2-norm bounded and jointly normal distribution, while a threshold may be chosen based on a priori knowledge of unknown input. A numerical example is given to demonstrate the effectiveness of the proposed method.