Abstract: A saddle clamp for mounting on a bone with curved surface in a bone-fixing or spinal fusion operation, for carrying a bone-fixing member. The saddle clamp has a rigid body with at least two holes for passing fixing elements to be tightened to the bone and at least one assembly element integral with the body for attaching the bone-fixing member. The rigid body has a contact surface configured to allow at least three points of contact with the curved surface of the bone when the saddle clamp is mounted thereon, at least two of the holes passing through the contact surface at least adjacent to two of the points of contact so as to provide, upon tightening of the fixing elements, at least three spaced apart, non-collinear areas of contact and thereby firm attachment of the saddle clamp to the bone.