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EEG data can be easily influenced by other components in the process of recording, which would thus interfere the analysis. Independent Component Analysis (ICA) is a valid method for blind source separation. It can estimate original signals' independent components from observed signals even the original signals and mixing model are unknown. Considering the shortcomings of the application of two ICA algorithms, FastICA and extended Infomax, to EEG artifacts removal, we propose a novel InfastICA algorithm by combing FastICA and extended Infomax. By appling to removal of the EOG artifacts from EEG, test results show that this new algorithm has no special requests to the matrix W's default values and study steps, and has a fast convergence speed, with simple operation and practical application.