Abstract: A method and apparatus for trephining corneal tissue is disclosed which reduces post-operative astigmatism in corneal transplant patients. A donor corneal-scleral button is accurately centered onto a concave surface by means of concentric rings and then held in place, preferably by suction. A rotating circular cutting blade is then lowered through the button to cut out a circular section which forms a donor button. An apparatus to carry out the method of the present invention comprises a curved surface for retaining the corneal-scleral button with circular indicia for positioning the button and apertures for applying a suction thereto. An upper part which is movable into and out of the space immediately above the curved surface mounts a motorized cutting device. The rotational speed and the lowering of the cutting device are controllable by the operator.