The invention concerns an intervertebral implant comprising: an intervertebralwedge (12) which is formed in one piece and has a body (18) with a longitudinal direction,having along this direction a first insertion face (22) and a second face (24),and two recesses (30, 32) arranged at the ends of the body, each recess being definedby a first extension (34) prolonging said insertion face, a second extension(36), and a bottom wall (38) and two fixation links (14, 16), each link havinga first end integral with said first extension (34) and a second end that can befixed to said second face in order to partially surround a spinous process andhold it in a recess. Each first extension (34) of the body has a height (h), relativeto the bottom wall of the recess, which is at most equal to the height (h)of the second extension that is associated with it and that is between 1 mm and 3mm.
