The inner-outer factorization of a non-square proper function which has infinite and finite j omega-axis zeros and has no poles in the open right-half plane is studied in this paper via the concept of an infinite zero compensator. For a stabilizable and detectable realization of the above function with full normal column rank, the eigenstructures of the system matrix pencils of the function and its spectral density matrix are discussed based on Kronecker's theory, and a simple state-space solution to the inner-outer factorization is given via the solutions of the generalized eigenvalue problems in terms of the original realization of the function.