The "cleaning-out" capability of a flat combing machine is increased by decreasing the distance between the jaw of the tong of the flat comber and the points of the opposed rows of needles on the round comber to a minimum distance and keeping this minimum distance constant. The needles are arranged on the round comber such that the radius of the needle points of the rows of needles lying side by side to the pivot of the round comber decreases, then increases, counter to the direction of rotation of the round comber. The tong is suspended by a pendulum and the distance between the pivot of the pendulum and the axis of the round comber is less than the sum of the maximum radius needle points to the pivot of the round comber, plus the minimum distance from the jaw of the tong to the needle points, plus the radius of the jaw of the tong to the pivot of the pendulum.