  The birefringence phenomenon in the vacuum with a constant magnetic
background of arbitrary strength is considered within the framework of the
effective action approach. A new feature of the birefringence in a magnetized
vacuum is that the parallel mode, which is polarized parallel to the plane
containing the magnetic field and the photon wave vector, is no longer
transverse. We have studied this feature in detail for arbitrary magnetic field
and provided analytic results for the ultra-strong magnetic field regime.
Possible physical implications of our results in astrophysics are discussed.
