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This technical note deals with the problem of finite horizon H∞ fault detection for linear discrete time-varying systems. Using an observer-based fault detection filter (FDF) with residual feedback as a residual generator, a new problem formulation of fault detection is first presented. Then the design of finite horizon H∞ -FDF is converted into a minimum problem of certain quadratic form. Through building a relationship with Krein space projection and applying innovation analysis, a sufficient and necessary condition for the minimum is derived and a solution to the H∞ -FDF is obtained by recursively computing Riccai recursions. Numerical examples are given to show the effectiveness of the proposed method.