Signals from extracellular electrodes in neural systems record voltages resulting from activity in many neurons. Detecting action potentials (spikes) in a small number of specific (target) neurons is difficult because many neurons, both near and more distant, contribute to the signal at the electrode. We consider some nearby neurons as target neurons (providing a signal) and all the other contributions to the signal as noise. A new algorithm for spike detection has been developed: this applies a cepstrum of bispectrum (CoB) estimated inverse filter to provide blind equalization. This technique is based on higher order statistics, and seeks to find a sequence of event times or delta sequence. We show that the CoB-based technique can achieve a 98% hit rate on an extracellular signal containing three spike trains at up to 0 dB SNR. Threshold setting for this technique is discussed, and we show the application of the technique to some real signals. We compare performance with four established techniques and report that the CoB-based algorithm performs best.