A suspensory fixation device has an elongated anchor member adapted to be transversely situated at the exit of a bone tunnel. A graft supporting loop member formed of a pair of parallel suture limbs extending from a bight portion is suspended transversely from the anchor member and has a loop length which is adjustable so the graft ligament can be supported in the bone tunnel at varying distances from the anchor member. When a graft ligament is attached to the saddle end of the loop member, the length of the loop member may be shortened by simply pulling distally on the pair of limbs at one end of the loop member to pull the graft ligament into the bone tunnel a predetermined distance or until it bottoms out at the floor of the bone tunnel. When tension is applied to the loop member by the graft pulling the loop proximally, the bight portion of the suture automatically locks the graft supporting loop member in place.