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We develop a wavelet-based action potential detection method to lower the level of signal-to-noise ratio (SNR) required for successful detection. It is based on point-wise product of wavelet coefficients of several scales, and effectively performs the role of combination of matched filters. We show its performance for various neural signal recordings. Detection of action potential from extracellular neural signal can be difficult due to the low SNR and high similarity between the target signal and noise. In previous studies or experimental neurophysiology using the extracellular recording, only the action potentials with sufficiently large amplitude have been gathered and analyzed. We compared its performance with those of the linear optimal filter and the Teager energy operator, and showed the superiority or the proposed detector over them. Test was performed for various SNR values and degrees or spectral similarity between the target signal and the noise.