A laser cleaving apparatus for use in terminating optical fiber cable ends has a laser beam source, the output of which is directed through a beam distorting member, which produces a beam having a chisel shape with a substantially flat side normal to the axis of a connector fiber containing ferrule and focuses it onto the fiber at a point adjacent the ferrule end face with the flat side also adjacent the end face. A single step polishing stage polishes the cleaved fiber end face to make it flat and flush with the ferrule end face.