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This paper deals with the problem of robust fault detection for a class of linear discrete time-varying (LDTV) systems subject to multiple packet dropouts. Under the assumption of data packets being time-stamped, the system under consideration can be described by an augmented LDTV systems without packet dropouts and, based on this, a parity space approach to fault detection of linear time invariant systems is extended to handle the problem of fault detection of the LDTV systems. Recursive algorithms are provided to reduce the computations of parameter matrices. A numerical example is given to show the effectiveness of the proposed method.