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A new brain source localization technique using electroencephalograms (EEGs) is investigated in this paper. The information which describes the location of certain known sources is used as the constraint within the proposed blind source separation (BSS) algorithm and leads to a solution to the ill-posed inverse problem of source localization. Non-homogeneity of the head tissues, on the other hand, is exploited by introducing a realistic model of the mixing system. This model is used to better identify the location of the unknown sources within the brain from projection of the separated independent components on to the scalp. A separate procedure is employed to highlight the rhythmic EEG sources such as Alpha rhythm as the known sources. The performance of the scheme is shown on real EEG measurements and compared with that of ldquo;conventional dipole fitting algorithmrdquo;.