  This report examines the thickness dependence of the reorientation phase
transition in ferromagnetic films with perpendicular anisotropy. That is, we
find the exact boundary of metastability of uniformly magnetized in-plane
states as the solution to a set of transcendental algebraic equations, and find
the profile of the initial instability in the magnetization in the direction
normal to the plane of the film. In general, this instability occurs at a
finite wave number k. We determine the dependence of k on the film thickness.
