Metal-induced crystallization has allowed for high-quality Si and Ge thin films on insulators at low temperatures; however, there has been difficulty for SiGe alloys of intermediate compositions.Here we demonstrate a large-grained (> 100 µm), 99% (111)-oriented Si0.4Ge0.6 layer on a glass substrate through layer exchange between Al and amorphous Si0.4Ge0.6 layers. Slow annealing below 350 °C is a key to suppressing nucleation and facilitating lateral growth. The use of the (111)-oriented SiGe layers as epitaxial templates will pave the way for integrating various materials monolithically on three-dimensional Si large-scale integrated circuits and on multi-functional displays.