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A scheme is proposed to construct the controlled-NOT gate in an ion-trap computer, based on the interaction of trapped-thermal ions with bi-chromatic laser fields.In this scheme, a specific laser pulse sequence for the implementation of this gate is given.Furthermore, it is pointed out that this laser pulse sequence is different from that of Ref.[3] [Phys.Rev.Lett.82 (1999) 1971), which cannot result in a real controlled-NOT gate.