A vertebral fixation device and corresponding method of fixation hold a spinal vertebra on a rod. The device has a fixation element including a component of substantially U-shaped cross section with a first branch, a bottom and a second branch. A loop is formed by a flexible band for connecting the vertebra to the component, and which passes through recesses provided in the branches. Adjustable means for immobilizing the flexible band are provided. Those means include a connector screw having a head for longitudinal immobilization of the screw with respect to the first branch a thread for screwing in the second branch. A removable sleeve for passage of the screw, insertable in the first branch, in longitudinal abutment with the head of the screw is provided and presents a chamfered part designed to cooperate with the rod to compress the band between the rod and the bottom of the component.
