  The phenomena of magneto-optical polarization rotation and circular magnetic
dichroism are well known in the Faraday configuration. We present another
effect, an odd magneto-optical linear dichroism, arising in nanostructures with
polarization-dependent mode Q-factors. It reveals itself as the magneto-optical
modulation of light intensity for the two opposite magnetization directions in
the Faraday configuration. The effect was demonstrated on a magnetophotonic
crystal with a cavity mode, the polarization-dependent Q-factor of which is due
to oblique incidence. For a polarization angle of 60{\deg} (or 120{\deg}) and
an angle of incidence around 60{\deg}, the magneto-optical intensity modulation
maximizes and reaches 6%.
