Both the icosahedral and decagonal phases have been found in AI13Cr4Si 4 melt-spun ribbons. A definite orientation relationship existing between these two phases is determined by SAD which is the same as that obtained previously by Schaefer and Bendersky. During the icosahedral quasicrystal-crystal transformation in this AI-Cr-Si alloy, the AI13Cr4Si 4 crystalline phase forms at low temperature and an unknown phase at high temperature. Both crystalline phases have definite orientation relationships with the icosahedral phase. The five-fold rotational twins of AI13Cr4Si 4 around the [1 1 0] direction formed from the icosahedral phase follow the group-subgroup relationship. The unknown phase has a hexagonal lattice, a = 0.73 and c = 1.62 nm.