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In this brief, the finite-horizon H∞ fault estimation problem is investigated for a class of uncertain linear discrete time-varying systems with known inputs. A new H∞ performance index including the known inputs is put forward in order to better reflect the effect of the known input on the whole fault estimation systems. To cope with the uncertainties, an auxiliary system is constructed with a certain indefinite quadratic form. By recurring to the Krein-space theory, the optimization problem of the associated indefinite quadratic form is solved, and a sufficient condition with much less conservativeness is established for the existence of the desired fault estimator. Then, all the estimator parameters are derived simultaneously in terms of an explicit solution to a matrix equation. Finally, an illustrative numerical example is employed to demonstrate the effectiveness of the proposed fault estimation scheme.