The invention relates to an intervertebral implant (1) provided with a central axis (2); comprising two U-shaped insertion parts (3, 4) which are arranged on top of each other in an axial manner in relation to the central axis (2) and which comprise base surfaces (15) which are oriented counter to each other, respectively a first and a second lateral surface (18, 19), respectively a ventral and a dorsal lateral surface (20, 21) and respectively an opposition surface (17) comprising a channel (13) which is used to receive the spinous processes (32) of two adjacent vertebral bodies (33, 34); an intermediate piece (5) which can be inserted in a transversal manner on the central axis (2) between the base surfaces (15). The intermediate piece (5) comprises two bearing surfaces (16) which can be placed on the base surfaces (15), and each bearing surface comprises a first three-dimensional structure (22a); and each of the base surfaces (15) comprises a second three-dimensional structure which can engage with the first three-dimensional structure (22a), such that the insertion pieces (3; 4), when the first and second structures (22a; 22b) are engaged, can be detachably fixed to the intermediate piece (5) which is parallel to the central axis (2). The insertion pieces (3, 4) comprise, respectively, on the same lateral surface (18, 19), connecting means (23) which are used to secure the insertion pieces (3; 4) to the gripping elements (43) of a surgical instrument (35) and the first and the second structures (22a, 22b) can be engaged, respectively disengaged, only by the lateral surface (18, 19) comprising the connecting means (23).