The phenomenon of the free overfall, experimentally investigated since the pioneering work of H. Rouse (1933) but not enough known analytically, is studied here assuming the steady flow to be two-dimensional, irrotational and frictionless and accounting for the presence of two free curvilinear boundaries. We derive a more general equation than the known one valid for the flow over a flat bottom. By adopting this equation together with the conservation laws, we can deduce: (a) an equation for the lower profile of the nappe, (b) the value of the brink depth and (c) an equation for the free surface profile of the flow upstream from the brink depth. The results are confirmed by the already available experimental data and by new measurements of the author.