The Berreman matrix method is applied to determine the transmission and reflection characteristics of birefringent thin films. Standard boundary conditions are imposed on resultant electric- and magnetic-field vectors at interfaces. A simplified analytic expression for the 4×4 propagation matrix of a general homogeneous biaxial layers is derived. Thus simple matricial relations are obtained for transmitted and reflected electric-field amplitudes of birefringent thin films. These matricial recurrence relations include multiple reflections while dealing with total fields. This provides support for a more general anisotropic multilayer film system. Example calculations are presented for a special case of isotropic-biaxial-isotropic film system. And these should be the foundation of further research and the design of birefringent thin-film devices.