The drilling instrument (10), for cleaning and forming of radicular teeth canals, comprises an end section (11), mounted in a chuck and driven by an electric motor, a distal region (12), a central region (13), provided with cutting flutes (16) and a proximal region (14) with a rounded end (15), serving to guide the instrument in the canal. The envelope (20) around the proximal, central and distal regions has a generally inverted cone shape with a vertex angle (F) identical over the whole length thereof. The junction region (17) between the proximal region (14) and the end section (11) has an incipient fracture (18), calibrated such as to break on application of a given driving torque. The instrument eliminates all risk of jamming and hence breakage in the radicular canal.