The collet is formed by a metal band (10) whose inner contour (11) delimits the recesses (11a, 11b, 11c) for driving the collet onto a balance staff (2) and whose outer contour (12) includes a function point (4) between the collet and the balance spring (9) located at the end of an arm (14) at a distance R from the centre 0 of the staff (2) greater than that of any other point (6, 8, 13, 15, 17) of the outer contour (12). It is characterised in that the inner contour (11) includes a discrete number of points of contact (1, 3, 5, 7) with the staff (2) distributed along identical or different angular apertures .alpha. and in that width "I" of the band (10) varies such that the compression forces of the contact points (1, 3, 5, 7) on the staff (2) do not substantially alter the distance R after driving in, leading to a friction torque allowing angular orientation of the collet on the staff (2) and not introducing any unbalance.
