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Let T be the multiplier operator associated to a multiplier m, and [b, T] be the commutator generated by T and a BMO function b. In this paper, the authors have proved that [b, T] is bounded from the Hardy space H1 (Rn) into the weak L1 (Rn) space and from certain atomic Hardy space Hlb (Rn) into the Lebesgue space L1 (Rn), when the multiplier m satisfies the conditions of Hormander type.