Multiunit recording with a multi-electrode in the brain has been widely used in neuroscience studies. After the data recording, neuronal spikes should be sorted according to spike waveforms. For the spike sorting, independent component analysis (ICA) has recently been used because ICA potentially solves the problem to separate even overlapped multiple neuronal spikes into the single. However, we found that multiunit signals are recorded in each electrode channel with channel-specific delay. This situation does not satisfy the instantaneous mixture condition prerequisite for most of ICA algorithms. Actually, this delayed mixture situation was shown to degrade the performance of an ordinary ICA. In this study, in order to overcome this problem, complex-valued processing in the time-frequency domain is applied to multiunit signals by the wavelet transform. In the space spanned by the wavelet coefficients, the condition of instantaneous mixture is almost fulfilled. By application to a synthetic multiunit signal, the ICA algorithm extended to complex-valued signals makes much improvement in spike sorting performance so that even overlapped multiple spikes are successfully separated. Taken together, the complex-valued method could be a powerful tool for spike sorting.