A pivot organ (5a, 5b) designed to allow the rotation of a piece (3) of a clockwork movement around an axis of rotation, includes two elements: a pivot (7a, 7b) and a bearing (6a, 6b) receiving the pivot (7a, 7b), one being integral with the piece (3) and the other being integral with the frame (1) of the movement. The elements (6a, 6b, 7a, 7b) have shapes at their opposite surfaces such that the section of one of the elements along a plane perpendicular to the axis of rotation is circular, the section of the other element along the plane being non-circular, so as to reduce the contact surface between the pivot (7a, 7b) and the bearing (6a, 6b). At least the contact surfaces of the two elements against each other are made from at least one material intrinsically having a low coefficient of friction and a low wear coefficient.