A cut-off construction for a transverse fan assembly, including for use with agricultural combine harvesters, to permit the transverse fan assembly to be operated to provide increased air flow volume at a lower rotational fan speed, which cut-off construction includes generally planar inner surfaces on first and second body portions that are positioned laterally to one another along the top of the output throat of the air plenum of the transverse fan assembly between the outer periphery of the fan and a baffle construction of the transverse fan, such that the inner surface of the first body portion is disposed at a cut-off inclination angle α, dependent upon certain parameters of the fan, and the inner surfaces of the first and second body portions intersect with one another in such a way that an upper wall for the output throat is formed by the cut-off construction and by the baffle construction of the fan assembly, which upper wall has a concavity formed therein and therealong near the outer periphery of the fan that effects a shift of the steering vortex of the fan in such a way as to permit the fan to operate with increased air flow volume at lower rotational fan speed.