A method and apparatus for reconstructing a ligament. In one preferred form of the invention, there is provided 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 transverse fixation pin hole preferably extending substantially perpendicular to the longitudinal axis of the body. And in one preferred form of the invention, the invention also comprises an installation tool for inserting the graft ligament support block into the bone tunnel and, while supporting the graft ligament support block in the bone tunnel, forming a transverse tunnel in the host bone, with the transverse tunnel in the host bone being aligned with the transverse fixation pin hole in the graft ligament support block. In one preferred method of use, a graft ligament is looped through the graft hole in the graft ligament support block, and the graft ligament support block is mounted to the installation tool. Then the installation tool is used to advance the graft ligament support block 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 transverse fixation pin hole in the graft ligament support block. Then the graft ligament support block is secured in place by pinning the graft ligament support block within the tunnel, i.e., by advancing a transverse fixation pin along the transverse tunnel in the host bone and into the transverse fixation pin hole in the graft ligament support block. Then the installation tool is detached from the graft ligament support block, and the installation tool is withdrawn from the surgical site.