An expandable osteosynthesis implant has branches (5) each connected at one end to a seat (7) which is pierced by an orifice (8), suitable for being slid from a posterior direction between the facing faces of two consecutive vertebrae in order to hold them a given distance apart and restore stability of the spinal column. According to the invention, said branches (5) and said seat (7) define a hollow cage (1) which, in a “rest” position, has an outside general shape that is a cylinder of circular section, and a portion at least of the inside volume (9) of the cage (1) towards the distal ends of said branches (5) is in the form of a circular truncated cone whose large base is towards said seat (7) which implant has at least three branches (5) and, inside said inside volume (9) at least one spacer (2) suitable for passing through said orifice (8) and the large base of the truncated cone.