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This paper utilizes a discrete wavelet transform to present a parallel architecture for independent component analysis (ICA), which is a hybrid system consisting of two sub-ICA processes. One process takes the high-frequency wavelet part of observations as its input, meanwhile the other process takes the low-frequency part. Their results are then merged to generate the final ICA results. Compared to the existing ICA algorithms, the proposed approach utilizes the full observation information, but the effective input length of the two parallel processes is halved. It therefore generally provides a new way for fast ICA implementation. In this paper, the experimental result has shown its success in extracting the independent components from a mixture.