A compression plate for the retention and internal fixation of fragments resulting from a bone fracture. The compression plate is of generally elongate structure and is adapted to be attached to both pieces of the broken bone by screws fitting within slots generally aligned with the length of the compression plate. At least one of the slots in the compression plate is formed with a slot having a taper, generally defined by a portion of the arc of a first hole through the compression plate, a portion of the arc of a second hole through the compression plate, larger in diameter than the first hole and closer to the end of the plate, and lines which are tangential to both holes. The top surface of the tapered slot is preferably chamfered so as to better mate with a screw having a tapered head. Thus, tightening of the screw in the tapered hole causes progression of the compression plate along its axis to encourage and retain the fracture surfaces in firm abutment.