Transcranial magnetic stimulation (TMS) combined with electroencephalography (EEG) is a powerful tool for studying cortical excitability and connectivity. To enhance the EEG interpretation, independent component analysis (ICA) has been used to separate the data into independent components (ICs). However, TMS can evoke large artifacts in EEG, which may greatly distort the ICA separation. The removal of such artifactual EEG from the data is a difficult task. In this paper we study how badly the large artifacts distort the ICA separation, and whether the distortions could be avoided without removing the artifacts. We first show that, in the ICA separation, the time courses of the ICs are not affected by the large artifacts, but their topographies could be greatly distorted. Next, we show how this distortion can be circumvented. We introduce a novel technique of suppression, by which the EEG data are modified so that the ICA separation of the suppressed data becomes reliable. The suppression, instead of removing the artifactual EEG, rescales all the data to about the same magnitude as the neural EEG. For the suppressed data, ICA returns the original time courses, but instead of the original topographies, it returns modified ones, which can be used, e.g., for the source localization. We present three suppression methods based on principal component analysis, wavelet analysis, and whitening of the data matrix, respectively. We test the methods with numerical simulations. The results show that the suppression improves the source localization.