Abstract: 1. The thread cutting insert (10) includes a laterally projecting tooth (30) comprising a front, chip cutting and repelling face (31), delimited by a cutting edge (31A) separating it from a flank area with a profile (33) having a determined overall relief angle (D), characterised by the fact that the tooth comprises, rearwards of a forward volume part (30A) directly supporting the cutting edge (31A) and limited by the flank area extending over a limited thickness (h1), a part (30B) for bracing the forward volume part (30A), having a profile (36) with an average relief angle differing from the overall relief angle (D) of the profile (33) of the flank area.