A connection mechanism of a vertebral fixing system includes a bone fixing device having its near end as a connection end and its far end for fixing the spinal segment to be fixed, in which the connection end comprises a receiving portion a first connecting rod having at least one end as a joining end, and the outer side of the joining end near the rod end is substantially spheral shaped and the rod end has a spheral bulge a second connecting rod having at least one end as a joining end, in which the outer side of the joining end near the rod end is substantially spheral shaped, and the rod end has a spheral groove for matching with the spheral bulge of the first connecting rod a first connecting cup having a connection mechanism at the cup opening edge, in which the inner side of the cup bottom is at least partially substantially spheral shaped, and the curvature of the spheral shape is slightly smaller or substantially equal to the curvature of spheral shape of the outer side of the joining end of the first connecting rod near the rod end for being universally joined with the spheral shape of the outer side of the first connecting rod near the rod end, and the cup bottom has a through hole for allowing the rod of the first connecting rod to extend outside from inside of the connecting cup a second connecting cup having a connection mechanism at the cup opening edge, in which the inner side of the cup bottom is substantially spheral shaped, and the curvature of the spheral shape is slightly smaller or substantially equal to the curvature of the spheral shape of the outer side of the joining end of the second connecting rod near the rod end for being universally joined with the spheral shape of the second connecting rod near the rod end, and the cup bottom has a through hole for allowing the rod end of the second connecting rod to penetrate outside from inside of the connecting cup and, a fastener for fixing the connecting cups with the receiving portion of the bone
