Most available methods for endmember extraction use the convexity of the data structure and consider the vertices of the data as the purest pixels. Such methods do not consider the applicability of the linear mixing model once the endmembers have been extracted. Thus they might return false endmembers if the data contain outliers such as anomalies. In this paper we tackle this problem by identifying endmembers in a robust way, separating them from outliers. We tested the proposed algorithm with real and synthetic data and compared it with the VCA, SGA and N-FINDR algorithms, showing better and more robust endmember extraction.