Spinel single crystal filaments are produced by a method which consists essentially of solidifying in one direction a melt consisting essentially of 30 to 70% by weight of magnesium oxide, 10 to 45% by weight of aluminum oxide, and 15 to 45% by weight of silicon dioxide, thereby forming a composite texture containing a matrix of forsterite and filaments of spinel dispersed in the matrix, and then separating the filaments of spinel from the composite texture.