  The light-induced frequency shift due to the hyperpolarizability (i.e. terms
of second-order in intensity) is studied for a forbidden optical transition,
$J$=0$\to$$J$=0. A simple universal dependence on the field ellipticity is
obtained. This result allows minimization of the second-order light shift with
respect to the field polarization for optical lattices operating at a magic
wavelength (at which the first-order shift vanishes). We show the possibility
for the existence of a magic elliptical polarization, for which the
second-order frequency shift vanishes. The optimal polarization of the lattice
field can be either linear, circular or magic elliptical. The obtained results
could improve the accuracy of lattice-based atomic clocks.
