An endodontic instrument (20) for drilling root a canal within a tooth. The instrument has a working area (21) that is arranged so as to form, shape and/or cut the inner wall of the root canal. The instrument has a plurality of flutes wound around a central axis in the form of a spiral, within a conical envelope (25) so as to have a cross-section that becomes narrower from a first end (23) to the second end (26) of the instrument. The working area (21) is sub-divided into adjacent segments (13) such that the flutes alternately have a straight section and a section that is twisted in the form of a spiral and are arranged, in such a way, that the edges of the flutes are located either on the conical envelope (25) or inside the envelope on the straight sections or on the twisted sections.