The invention concerns a drilling instrument (10), in particular for drilling dental root canals comprising a base (11) and a guide section (13) as well as a polygonal cutting section (12). Said cutting section includes several helical cutting edges (17) defining an envelope (15). The flutes (14), which are the surfaces linking in the cutting edges, are cut out such that part of them define clearance zones (16a) alternately arranged between the drilling zones (16b). In the central part of a clearance zone (16a), the cutting edges (17) are all arranged recessed inside the envelope (15), in the central part of the drilling zone (16b), said cutting edges are all arranged on the envelope, and in a zone intermediate between a clearance zone (16a) and an adjacent drilling zone (16b), at least one cutting edge is on the envelope and at least one cutting edge is recesses inside the envelope.