Multiunit recording has been widely used in neuroscience studies. In this recording, some spike-sorting method is required. For the spike-sorting, independent component analysis (ICA) has recently been used because ICA potentially separates overlapped multiple neuronal spikes into the singles. However, multiunit signals are recorded in each electrode channel possibly with channel-dependent waveform transformation (spatio-temporal mixture). This situation does not satisfy the instantaneous mixture condition prerequisite for most of ICA algorithms. To address this problem, we have proposed a novel spike sorting method incorporating wavelet transform and complex-valued ICA and have evaluated the performance. In this paper, firstly we compared proposed method with the real-valued ICA-based method by applying them to a synthetic multiunit signal. This application result showed that the ICA algorithm extended to complex-valued signals makes much more improvement in spike sorting performance. However, the accuracy of spike-sorting decreases commonly in both ICA-based methods, as S/N ratio becomes lower. Further investigation disclosed a possible mechanism that the noise disturbs accurate estimation of the basis vectors for separation. To the actual multiunit signals, our method outperformed the real-valued ICA-based method as well. Shortly, although the proposed method can solve the spatio-temporal mixture, it should equip with robustness against noise and should be improved for handling over-complete situations. For this to be realized, a hybrid method combining a pattern recognition-based method with the proposed method will be one of valuable options in the future.