In most approaches to speech recognition, the speech signals are segmented using constant-time segmentation, for example into 25 ms blocks. Constant segmentation risks losing information about the phonemes. Different sounds may be merged into single blocks and individual phonemes lost completely. A more satisfactory approach is to attempt to segment the phoneme boundaries from the speech signals and use these boundaries to define blocks. The discrete wavelet transform (DWT) is interesting in the analysis of speech since it is easy to extract parameters which take into account the properties of the human hearing system. The analysis of the power in different frequency bands offers potential for distinguishing the start and end of phonemes. For many boundaries, there is no discernible drop in overall power, and at some frequencies, the power is broadly constant over the lifetime of the phoneme. However, many phonemes exhibit rapid changes in particular subbands which can be used to detect their start and endpoints. In this paper we apply the DWT to speech signals and analyse the resulting power spectrum and its derivatives to locate candidates for the boundaries of phonemes in continuous speech. We compare the results with hand segmentation and constant segmentation over a number of words. The method proves effective for finding most phoneme boundaries.