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The mu rhythm is an electroencephalogram (EEG) signal located at the central region of the brain that is frequently used for studies concerning motor activity. Quite often, the EEG data are contaminated with artifacts and the application of blind source separation (BSS) alone is insufficient to extract the mu rhythm component. We present a new two-stage approach to extract the mu rhythm component. The first stage uses second-order blind identification (SOBI) with stationary wavelet transform (SWT) to automatically remove the artifacts. In the second stage, SOBI is applied again to find the mu rhythm component. Our method is first compared with independent component analysis with discrete wavelet transform (ICA-DWT) as well as SOBI-DWT, ICA-SWT, and regression method for artifact removal using simulated EEG data. The results showed that the regression method is more effective in removing electrooculogram (EOG) artifacts, while SOBI-SWT is more effective in removing electromyogram (EMG) artifacts as compared to the other artifact removal methods. Then, all the methods are compared with the direct application of SOBI in extracting mu rhythm components on simulated and actual EEG data from ten subjects. The results showed that the proposed method of SOBI-SWT artifact removal enhances the extraction of the mu rhythm component.