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Endmember extraction has received increasing interest in hyperspectral image analysis. One widely used endmember extraction algorithm is pixel purity index (PPI), which finds endmembers via a set of random vectors, called skewers. Several issues arise in its implementation. One is the prior knowledge of the number of skewers K required to be used. Second, due to random nature in skewers, the final results are inconsistent and unreproducible. Third, it needs to know the number of dimensions to be retained after dimensionality reduction. Fourth, it needs to preset a cutoff threshold to extract potential endmembers. Finally, it involves human intervention to manually select final endmembers. This letter derives a random PPI (RPPI) to resolve the aforementioned issues. It considers the result produced by PPI using a random set of initial vectors as skewers as a realization of a random algorithm. From a statistical signal processing view point, if endmembers are crucial in terms of information, they should occur in realizations produced by PPI regardless of what set is chosen for skewers. By virtue of this assumption, the proposed RPPI is developed and validated by experiments.