The introduction of Arterial Spin Labelling (ASL) techniques in Magnetic Resonance Imaging (MRI) has made feasible a non-invasive measurement of the Cerebral Blood Flow (CBF). However, to date, the low signal-to-noise ratio of ASL gives us no option but to repeat the acquisition to accumulate enough data in order to get a reliable signal. The perfusion signal is then usually extracted by averaging across the repetitions. But the sample mean is very sensitive to outliers. A single incorrect observation can therefore be the source of strong detrimental effects on the perfusion-weighted image estimated with the sample mean. We propose to estimate robust ASL CBF maps with M-estimators to overcome the deleterious effects of outliers. The behaviour of this method is compared to z-score thresholding as recommended in [1]. Validation on simulated and real data is provided. Quantitative validation is undertaken by measuring the correlation with the most widespread technique to measure perfusion with MRI: Dynamic Susceptibility weighted Contrast imaging.