The handle and a curved rotatable cartridge are provided with shaving blades positioned on both sides of the curved cartridge. The cartridge is rotatably mounted to the handle and is held in either concave or convex shaving positions with detents. When the alternate shaving position is desired, the cartridge is rotated 180 degrees, either manually or remotely using a push button device within the handle, which is also disclosed. The correct angular relationship of the handle to the cutting surface of the cartridge is set and maintained for both concave and convex settings.