Birefringence complicates the use and measurement of the Faraday effect. The Faraday rotation in nonbirefringent materials increases linearly with path length of the light propagation. However, the observed Faraday rotation in birefringent crystals oscillates about zero as a function of the light path length. A new experimental technique has been developed for measuring the intrinsic Faraday rotation and the birefringence of noncubic materials. The measurements are based on mathematical curve fitting of the oscillatory variation of the Faraday rotation as a function of the angle between the light-propagation direction and an optic axis in a sample with fixed uniform magnetization. The birefringence can be determined from the periods and the intrinsic Faraday rotation from the amplitudes of the oscillations. The oscillatory variations of the Faraday rotation in birefringent crystals suggest ways of optimizing the usefulness of the rotation.