Spike sorting is the mandatory first step in analyzing multi-unit recording signals for studying information processing mechanisms within the nervous system. Extracellular recordings usually contain overlapped spikes produced by a number of neurons adjacent to the electrode, together with background noise having unknown properties. In the present study, a robust method to deal with these problems is proposed. The method employs an automatic overlap decomposition technique based on the relaxation (RELAX) algorithm that requires simple fast Fourier transforms (FFT's). The performance of the presented system was compared with that of a previously published method and tested at various signal-to-noise ratio (SNR) levels based on synthetic data that were generated from real data.