  The Ritus' $E_{p}$ eigenfunction method is extended to the case of spin-1
charged particles in a constant electromagnetic field and used to calculate the
one-loop neutrino self-energy in the presence of a strong magnetic field.From
the obtained self-energy, the neutrino dispersion relation and index of
refraction in the magnetized vacuum are determined within the field range
$m_{e}^{2}\ll eB\ll M_{W}^{2}$. The propagation of neutrinos in the magnetized
vacuum is anisotropic due to the dependence of the index of refraction on the
angle between the directions of the neutrino momentum and the external field.
Possible cosmological implications of the results are discussed.
