If a steady jet with two free streamlines ascends a sill while entirely remaining on one sloping side, then the rising motions must be compensated by transverse sinking motions in order that the cross-stream integral of relative vorticity vanishes at all downstream sections. The maximum sill height which allows such a flow is computed assuming slow downstream changes in a quasi-geostrophic barotropic model; a 112 layer baroclinic model is also considered. If the critical sill height is exceeded, it is suggested that the jet will split with only part of it crossing the sill on the original side. This might explain why the Antarctic Circumpolar Current bifurcates at the Falkland Plateau, where one branch forms the Malvinas Current and the other branch turns eastward across the Atlantic. The theory is related to previous laboratory observations in which bifurcation occurs. ¿ 1997 American Geophysical Union