An improved matrix method of calculating the solutions of wave equations in a horizontally stratified anisotropic medium is described. An inhomogeneous medium is divided into a number of thin horizontal and homogeneous slabs. The solutions of a differential equation with constant coefficients in each slab are connected by applying the boundary conditions, and the wave fields are given as the power series expansion of wave fields. In calculating the wave fields, a matrix is divided into two matrices for two independent solutions and Gram-Schmidt orthogonalizing process is applied to prevent numerical swamping. Comparisons are made between this and other full wave methods regarding step size and computer time, and this method is found to be more efficient than the full wave method especially at high frequency wave fields. The magnetoionic modes separated from the resultant wave are shown for a model ionosphere.