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This paper is concerned with state estimation problem for discrete-time Markov jump linear systems. A novel recursive algorithm for estimating the state of the considered systems is obtained. Compared with the existing estimation algorithms for the systems under consideration, the novelty of the derived algorithm lies in using a bank of conditional expectation sets instead of a bank of Kalman filters to estimate the state. The algorithm is finite-dimensionally computable, and does not increase computation and storage capabilities in the number of the noise observation sequence. A numerical comparison of the algorithm with the interacting multiple model (IMM) algorithm is given.