A liquid-crystal switch capable of switching nearly 100% of unpolarized light from one multimode fiber to another had been conceived and demonstrated experimentally. The switch uses a double interaction with a single layer of nematic liquid crystal in which the liquid alignment is initially in plane at 90 degrees to the light propagation. This four-fiber optical reversing switch has a simple structure, a low insertion loss, and a low operating voltage. It should find a wide range of applications in fiber-optic communication systems.