A surgical implant (22) used to fix a ligament transplant (18) adapted to connect two bones on either side of a joint. The ligament transplant is fixed in a tunnel (10, 16) pierced from the outer cortical wall of a first bone and extending through a pre-determined depth of a second bone. The implant includes a first end (24) to be fixed to the transplant and a second end in the form of a hook (26) adapted to rest on an outer periphery (28) of the first bone's cortical part at the tunnel's inlet. The hook includes two lugs (30 and 32) adapted to be disposed on either side of the tunnel inlet so the hook rests on solid bone and not on bone having a reduced thickness at the tunnel's position, the axes of the lugs preferably being orthogonal to the hook's plane. One such implant is particularly suitable for replacing the knee's anterior cruciate ligament.