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A new endmember extraction method has been developed that is based on a convex cone model for representing vector data. The endmembers are selected directly from the data set. The algorithm for finding the endmembers is sequential: the convex cone model starts with a single endmember and increases incrementally in dimension. Abundance maps are simultaneously generated and updated at each step. A new endmember is identified based on the angle it makes with the existing cone. The data vector making the maximum angle with the existing cone is chosen as the next endmember to add to enlarge the endmember set. The algorithm updates the abundances of previous endmembers and ensures that the abundances of previous and current endmembers remain positive or zero. The algorithm terminates when all of the data vectors are within the convex cone, to some tolerance. The method offers advantages for hyperspectral data sets where high correlation among channels and pixels can impair un-mixing by standard techniques. The method can also be applied as a band-selection tool, finding end-images that are unique and forming a convex cone for modeling the remaining hyperspectral channels. The method is described and applied to hyperspectral data sets.