In this paper, we propose a novel speech enhancement (SE) method by exploiting the discrete wavelet transform (DWT). This new method reduces the amount of fast time-varying portion, viz. the DWT-wise detail component, in the spectrogram of speech signals so as to highlight the speech-dominant component and achieves better speech quality. A particularity of this new method is that it is completely unsupervised and requires no prior information about the clean speech and noise in the processed utterance. The presented DWT-based SE method with various scaling factors for the detail part is evaluated with a subset of Aurora-2 database, and the PESQ metric is used to indicate the quality of processed speech signals. The preliminary results show that the processed speech signals reveal a higher PESQ score in comparison with the original counterparts. Furthermore, we show that this method can still enhance the signal by totally discarding the detail part (setting the respective scaling factor to zero), revealing that the spectrogram can be down-sampled and thus compressed without the cost of lowered quality. In addition, we integrate this new method with conventional speech enhancement algorithms, including spectral subtraction, Wiener filtering, and spectral MMSE estimation, and show that the resulting integration behaves better than the respective component method. As a result, this new method is quite effective in improving the speech quality and well additive to the other SE methods.