New transmission properties of a magnetized ferrite slab are investigated theoretically for an oblique incident H plane wave. When the direction of magnetization is normal to the plane of incidence, there is single refraction. For magnetization parallel to the plane of incidence, then double refraction leads to a double beam of microwaves at the exit surface. If the electromagnetic field vectors of these two beams can be made orthogonal then after the beams exit the ferrite slab they can be independently modulated and subsequently analyzed and demodulated at a remote receiver. It was found that the two transmitted beams are contrarotating and elliptically polarized. The required interrelationship of the transmission coefficients was determined for cross polarization. The analysis not only explains the double refraction effect but also defines new transmission coefficients that can be used to evaluate the components of the transmitted waves.