  A complete solution of the ground-state problem for an Ising model on the
Shastry-Sutherland lattice with an additional interaction along the diagonals
of "empty" squares in an applied magnetic field is presented. A rigorous proof
is given that this interaction gives rise to a plateau at one-half of the
saturation magnetization. Such a fractional plateau has been observed in some
rare-earth-metal tetraborides, in particular, in strong Ising magnets ErB4
(where it is the only one) and TmB4 (where it is the broadest one), but its
origin has remained unclear. Our study sheds new light on the solution of this
problem.
