A system for setting and intersomatically fusing vertebrae comprises at least one case and a plate perpendicularly adjacent to the main plane of said case, wherein said plate (1) and case (2) are provided with a hole (21)and a stud (12) insertable and releasable lockable into said hole 21, the plate (1) is removable by a simple traction and a disassembling device and a kit comprises a system for setting and intersomatically fusing vertebrae and the disassembling device.