An endodontic instrument for drilling root canals, in particular a flexible drilling instrument which includes a working part and a securing end fitting intended for mounting the instrument in a mandrel of a contra-angle-type support provided with an electric motor used to drive an instrument clockwise. The casing of the working part is conical along its length and ends in a tip. The working part is provided with a spiral flute forming a ridge having a cutting edge. The drill bit, relief and cutting angles defined by the cutting edge can be varied along the length of the working part so that the instrument is particularly sharp in the area near the tip and so that the profile of the cutting ridge becomes progressively more blunt along the length of the instrument.