In this paper, we propose a new numerically reliable computational approach to determine the inner-outer factorization of a rational transfer matrix G of a linear descriptor system, In contrast to existing computationally involved "one-shot" methods which require the solution of Riccati or generalized Riccati equations, the new approach relies on an efficient recursive zeros dislocation technique. The resulting inner and outer factors always have minimal order descriptor representations. The proposed approach is completely general, being applicable whenever G is proper/strictly proper or not, or of full column/row rank or not.