PROBLEM TO BE SOLVED: To provide an osteosynthesis system (2) for joining at least two vertebrae which can be fitted more easily especially in a type having a fixing element in each vertebra.SOLUTION: A fixing element includes: a first nail (14) inserted into a first vertebra (4) by impact insertion a second nail (16) inserted into a second vertebra (6) by impact insertion, which is substantially on the same plane as the first nail (14), and is substantially parallel to the first nail (14) first and second fixing dowels (8 and 12) associated with the first and the second nails (14 and 16) respectively, the purpose of the dowels (8 and 12) being expanding during the insertion of the nails (14 and 16) into the dowels (8 and 12) and a bridge (18) firmly connected to the first and second nails (14 and 16). Each of the nails (14 and 16) is connected to the bridge by substantially spherical head part (44).