The drilling device for forming an osseous channel (2) with a curved profile (2b) via a straight cannula (6) previously fixed in the body of a vertebra (3) with a cortical plateau (4) of a spinal segment (Sr) of a vertebral column (Cv) includes a guide pin (8) which is provided from a guide pin kit and has at one of its ends a curved profile (8a) of which the radius of curvature R is less than 20 millimetres, and a sharpened tip (8b) arranged in a direction defined by an angle Y which is less than 90 degrees to the longitudinal axis of said pin, the profile of said guide pin (8) making it possible to define, after insertion thereof into the body of the vertebra (3), two contact points a and b ensuring the guidance of the free end of an articulated drill bit (10) so as to position said free end in a direction substantially perpendicular to that of the cortical plateau (4) of the vertebra (3) to be drilled.
