  We predict theoretically and demonstrate experimentally an
ellipticity-dependent nonlinear magneto-optic rotation of
elliptically-polarized light propagating in a coherent atomic medium. We show
that this effect results from a hexadecapole and higher order momenta of atomic
coherence, and is associated with an enhancement of Kerr and higher orders
nonlinearities accompanied by suppression of the other linear and nonlinear
susceptibility terms of the medium. These nonlinearities might be useful for
quantum signal processing. In particular, we report an observation of an
enhancement the polarization rotation of elliptically polarized light resonant
with the 5S_{1/2} F=2 -> 5P_{1/2} F=1 transition of Rb87.
