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Accurate estimation of impedance functions is essential for the correct interpretation of Controlled Source Audio Magnetotelluric (CSAMT) measurements. Noise is inevitably encountered when CSAMT observations are conducted and, consequently, impedance estimates are usually based on least-squares (LS) approximation. However, estimation procedure based on LS would not be statistically optimal, as outliers (abnormal data) are frequently superimposed on a normal ambient CSAMT noise field, which is approximately Gaussian. In this situation, the estimation can be seriously misleading. It is then essential to use statistical procedures that are robust in the sense of being resistant or insensitive to the presence of the outliers. An alternative method for making robust estimates of CSAMT impedance functions is based on M-estimators. In the resulting estimates, outlier contamination is removed. Using noisy synthetic data, it is shown that the proposed method can produce usable CSAMT impedance functions even under condition of severe outlier contamination.