An expandable osteosynthesis implant has branches each connected at one end to a seat which is pierced by an orifice, 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. The branches and the seat define a hollow cage 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 of the cage towards the distal ends of the branches is in the form of a circular truncated cone whose large base is towards the seat, which implant has at least three branches and, inside the inside volume at least one spacer suitable for passing through the orifice and the large base of the truncated cone.