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This paper discusses the applicability of the wavelet transform for analyzing EMG signal and discriminating motion classes. In previous many works, researchers have dealt with steady EMG and have proposed analyzing methods being suitable for the EMG, for example FFT and STFT. Therefore, it is difficult for the previous approaches to discriminate motions from the EMG in the different phases of muscle activity, i.e., pre-activity, in activity, post-activity phases, as well as the period of motion transition from one to another. In this paper, we introduce the wavelet transform using the Coiflet mother wavelet into our real-time EMG prosthetic hand controller for discriminating motions from steady and unsteady EMG. A preliminary experiment to discriminate three hand motions from four channels EMG in the initial pre-activity and in activity phase is carried out to show the effectiveness of the approach. However, future research effort is necessary to discriminate more motions much precisely.