In a headbox system for a papermaking machine with an adjustable distribution of the fiber stock suspension or pulp over the web width, the flow in the delivery slice is controlled in such a way that, across the web width, also the distribution of the fibers in respect of fiber orientation and quantity has a desired profile. For this purpose, the flow of the fiber stock suspension is controlled such that in the event of a change in the distribution of the fiber stock suspension across the web width, the horizontal component of the flow direction in the delivery slice remains, at all locations, always in the predetermined machine direction and thus transverse flows are avoided and the flow rate in the delivery slice has a predeterminate profile.