Abstract: The self-centering collet makes it possible to obtain a very high precision which makes it possible to grip, for example, bits with a diameter less than 0.3 mm with extremely small tolerances thanks to two arrangements: the first, by depressing in the middle zone (BC) the outside conical surface (AD) of the central body of collet (1) or of collet-holder (7) so that, with the collet closed, the two complementary surfaces touch one another only in their end parts (AB and CD); the second, in making ring nut (6) press on head (1") of central body (1) of the collet only along a circular rim (G) located near axis (EF).