Given rational matrix functions, G, H, and R, a necessary and sufficient condition is given for the existence of a causal solution to the equation GXH=R. A formula is given for a solution of the equation when it exists, and this particular solution is used to parameterize the set of all causal solutions of the equation. The results are specialized to the case when the function G is identically equal to identity. Applications of the author's results include exact model matching and disturbance decoupling problems.<>