For the analysis of multiunit extracellular neural signals as multiple spike trains, neural spike sorting is essential. Existing algorithms for the spike sorting have been unsatisfactory when the signal-to-noise ratio(SNR) is low, especially for implementation of fully-automated systems. We present a novel method that shows satisfactory performance even under low SNR, and compare its performance with a recent method based on principal component analysis(PCA) and fuzzy c-means(FCM) clustering algorithm. Our system consists of a spike detector that shows high performance under low SNR, a feature extractor that utilizes projection pursuit based on negentropy maximization, and an unsupervised classifier based on Gaussian mixture model. It is shown that the proposed feature extractor gives better performance compared to the PCA, and the proposed combination of spike detector, feature extraction, and unsupervised classification yields much better performance than the PCA-FCM, in that the realization of fully-automated unsupervised spike sorting becomes more feasible.