Abstract: The locality of wavelet makes itself focus on the partial structure of the signal. Therefore, the wavelet transformation can be used to determine the location of mutation of signals such as impulsive noise of machine causing by impulsive vibration. However, further research discovered that the single sub-band algorithm improved from wavelet transformation could recognize the mutation point of the first type effectively, but it could not recognize the mutation of second type, and furthermore, the fast algorithm of binary discrete wavelet transformation has issues such as frequency aliasing. This paper proposed improved single sub-band reconstruction algorithm, and resolved the issue of recognizing the transient signal of the second type by introducing transition functions. The effectiveness of this method was proved by related experiments.