A method and apparatus for reconstructing a ligament using a graft ligament support block which comprises a body, and a graft hole and a transverse fixation pin hole extending through the body, with both the graft hole and the fixation pin hole preferably extending substantially perpendicular to the longitudinal axis of the body. A graft ligament is looped through the graft hole, and the support block is advanced into the bone tunnel, with the two free ends of the looped graft ligament extending back out the bone tunnel. Next, a transverse tunnel is formed in the host bone, with the transverse tunnel being aligned with the fixation pin hole. Then the support block is secured in place by pinning the support block within the tunnel, i.e., by advancing a fixation pin along the transverse tunnel in the host bone and into the fixation pin hole in the support block.