Spike sorting is the mandatory first step in analyzing multiunit 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 unknown background noise, which in turn induce some difficulties in neural signal identification. In this paper, we propose a robust method to deal with these problems, which employs an automatic overlap decomposition technique based on the relaxation algorithm that requires simple fast Fourier transforms. The performance of the presented system was tested at various signal-to-noise ratio levels based on synthetic data that were generated from real recordings.