Recently, we developed a novel approach for blind source separation in multichannel signal processing environments [1]. The technique, which relies on an inherent invariance property of the signal subspace across multiresolution levels obtained in the wavelet transform domain, showed robustness to amplitude and shift variations encountered in multi-unit neural recording environments. In this work, we extend the work in [1] to describe in details a fast implementation of the algorithm and outline the criterion based on which the characterization of each source should be formulated. Results and performance evaluation that were not reported in [1] are illustrated in this paper.