Abstract: The purpose of the invention is a cross flow fan comprising an convergent inlet (2,3,10), an impeller (1) or rotor provided with blades and a divergent (4) delimited by a downstream face (12) of the scroll element and a downstream face (9) of the cross-head element. The inlet and divergent delimit two narrowing longitudinal passages (13, 14). With respect to a reference system of perpendicular axes x and y, the origin of which is located on the axis of rotation of the impeller (1) and whose abscissa X axis is parallel to the downstream face (9) of the cross-head element, it features:an upstream leading edge (6) of the cross-head element describing an angle included between 290.degree. and 330.degree. at a distance from the impeller or an air gap (13) included between 2 and 8% of the outside diameter De of the impeller,a face (7) of the cross-head element describing an angle, the apex of which is one and the same with upstream leading edge (6) of the cross-head, included between -20.degree. and 60.degree.