Automatic and accurate detection of action potentials of unknown waveforms in noisy extracellular neural recordings is an important requirement for developing brain-computer interfaces. This study introduces a new, wavelet-based manifestation variable that combines the wavelet shrinkage denoising with multiscale edge detection for robustly detecting and finding the occurrence time of action potentials in noisy signals. To further improve the detection performance by eliminating the dependence of the method to the choice of the mother wavelet, we propose an unsupervised optimization for best basis selection. Moreover, another unsupervised criterion based on a correlation similarity measure was defined to update the wavelet selection during the clustering to improve the spike sorting performance. The proposed method was compared to several previously proposed methods by using a wide range of realistic simulated data as well as selected experimental recordings of intracortical signals from freely moving rats. The detection performance of the proposed method substantially surpassed previous methods for all signals tested. Moreover, updating the wavelet selection for the clustering task was shown to improve the classification performance with respect to maintaining the same wavelet as for the detection stage.