An osseous anchoring implant, various embodiments of which comprise an osseous anchor and a head bearing fixation structure capable of receiving and fixing at least one bar, the head of the implant being traversed by at least one duct, which receives the bar through a lateral aperture, and by a threaded channel, whose axis is not parallel to the axis of the duct, which receives a fixation screw of the bar, the implant being characterized in that it comprises fixation structure of the head on the part of the implant which extends from the osseous anchor, these fixation structures allowing, prior to blocking and fixing, at least a determined mobility of the head around at least one axis not parallel to the axis of symmetry of the osseous anchor. The fixation screw of the bar may comprise a ball and socket at its base.