The exact bit error probability of a matched filter receiver in a known discrete Rayleigh fading multipath channel is determined for a binary antipodal system. The matched filter receiver or the RAKE is one form of a diversity receiver. Traditionally, both the interpath interference (IPI) and the intersymbol interference (ISI) caused by the non-ideal autocorrelation function of the bit waveform are neglected in the analysis of the RAKE. Previously, the exact matched filter bounds; which include IPI, were derived. This bound gives the performance of the matched filter if only one symbol is transmitted. In our analysis, a symbol sequence is transmitted instead of only one symbol. Thus, our analysis includes both IPI and ISI as well as the correlation between the paths, The analysis permits direct comparisons between different kinds of bit waveforms.