Single crystals of a CuSe alloy have been produced by a new technique. It is found that this alloy exists in two modifications which can be described as the 2H and 12H structures. Evidence and arguments have been presented to show that the 12H structure stabilizes owing to shear produced in the basic 2H structure. Detailed atomic positions of both basic and modified structures have been worked out. Good agreement has been obtained between the theoretical and experimental values of the intensities.