An intervertebral implant comprising: - a stabilizing wedge adapted to stabilize at least two adjacent vertebrae by interposition between spinous processes of said vertebrae, having a substantially parallelepipedal body which has a defined main axis, - at least one strap forming a flexible link for fixing the stabilizing wedge to the spinous processes of the vertebrae to be stabilized, said strap having first and second strap portions (41a, 42a) which each comprise one of the opposite ends (41, 42) of said strap, and said strap having a defined longitudinal direction and a defined strap surface, - at least one movable assembly adapted to come into engagement with the stabilizing wedge in such a way as to immobilize the strap with respect to the stabilizing wedge by clamping of said strap between said movable assembly and said stabilizing wedge, and - a locking member for axially locking the engagement of the movable assembly with the stabilizing wedge and thus the blocking of the strap, characterized in that - the body of the stabilizing wedge comprises at least one recess through which at least the first strap portion can pass, the recess having a longitudinal axis parallel to the main axis of the stabilizing wedge, and an inner wall extending parallel to said longitudinal axis of the recess with a defined shape; - the movable assembly comprises at least one blocking pin having a defined longitudinal axis and a defined shape substantially complementing the shape of the recess, in order to come into engagement with the stabilizing wedge by movement in said recess in the direction of the main axis of the body of said wedge in such a way that the longitudinal axis of the blocking pin: - firstly coincides with the longitudinal axis of the recess; - secondly is perpendicular to the longitudinal axis of the first strap portion inside the recess; and - thirdly is parallel to the surface of the first strap portion inside the recess, and moreover in such a way that the strap portion inside the recess is immobilized with respect to the stabilizing wedge by clamping of said strap portion between the blocking pin and the inner wall of the recess. - a stabilizing wedge adapted to stabilize at least two adjacent vertebrae by interposition between spinous processes of said vertebrae, having a substantially parallelepipedal body which has a defined main axis, - at least one strap forming a flexible link for fixing the stabilizing wedge to the spinous processes of the vertebrae to be stabilized, said strap having first and second strap portions (41a, 42a) which each comprise one of the opposite ends (41, 42) of said strap, and said strap having a defined longitudinal direction and a defined strap surface, - at least one movable assembly adapted to come into engagement with the stabilizing wedge in such a way as to immobilize the strap with respect to the stabilizing wedge by clamping of said strap between said movable assembly and said stabilizing wedge, and - a locking member for axially locking the engagement of the movable assembly with the stabilizing wedge and thus the blocking of the strap, characterized in that - the body of the stabilizing wedge comprises at least one recess through which at least the first strap portion can pass, the recess having a longitudinal axis parallel to the main axis of the stabilizing wedge, and an inner wall extending parallel to said longitudinal axis of the recess with a defined shape; - the movable assembly comprises at least one blocking pin having a defined longitudinal axis and a defined shape substantially complementing the shape of the recess, in order to come into engagement with the stabilizing wedge by movement in said recess in the direction of the main axis of the body of said wedge in such a way that the longitudinal axis of the blocking pin: - firstly coincides with the longitudinal axis of the recess; - secondly is perpendicular to the longitudinal axis of the first strap portion inside the recess; and - thirdly is parallel to the surface of the first strap portion inside the recess, and moreover in such a way that the strap portion inside the recess is immobilized with respect to the stabilizing wedge by clamping of said strap portion between the blocking pin and the inner wall of the recess. - firstly coincides with the longitudinal axis of the recess; - secondly is perpendicular to the longitudinal axis of the first strap portion inside the recess; and - thirdly is parallel to the surface of the first strap portion inside the recess,