(eng): The goal of this paper is to describe a Robust Artifact Removal (RAR) method - an automatic sequential procedure which is capable of removing short-duration, high-amplitude artifacts from long-term neonatal EEG recordings. Such artifacts are mainly caused by movement activity, and have an adverse effect on automatic processing of long-term sleep recordings. The artifacts are removed sequentially in short-term signals using ICA transformation and wavelet denoising. In order to gain robustness of the RAR method, the whole EEG recording is processed multiple times. The resulting tentative reconstructions are then combined. We show results in a data set of signals from ten healthy newborns. Those results prove, both qualitatively and quantitatively, that the RAR method is capable of automatically rejecting the mentioned artifacts without changes in overall signal properties such as the spectrum. The method is shown to perform better than either the wavelet-enhanced ICA or the simple artifact rejection method without the combination procedure.