Wavelet-based pattern classification methods, which have been used extensively in imaging applications, have barely been explored in machining monitoring and diagnostic systems. Although the engineering literature recognizes wavelet methodologies as a practical alternative to the FFT for signals containing nonstationary information, most of it concerns only the Wavelet Transform. The WT can detect time-localized pre-failure machining signals, but it leaves two practical questions unanswered. The first is how to post-process the wavelet coefficients (the WT output) to extract the needed information. The second is what method to use for 'scanning' the signal with overlapping windows, since the WT covers only a short segment of the input signal. The Matching Pursuit (MP) approach handles both of these problems in a straightforward manner. As a pattern recognition method, it is adaptable to specific machining diagnostic tasks and eliminates the post-processing requirement. The scanning technique is likewise built into the algorithm, making customized windowing methods unnecessary. MP methods, which are widely used in imaging applications such as face recognition, are easily adapted to one-dimensional signals. Moreover, the MP framework can be tailored to the needs of specific applications through several parameters, such as the wavelet family, which are left to the user's discretion. In this paper, we present an MP implementation for small drill-bit breakage prediction. During bit failure, the small-bit thrust cutting force signal is characterized by two types of transients. We show that the MP detects these transients more effectively than an earlier method (also devised by the authors) based on the Discrete Wavelet Transform (DWT).