The (J,J')-lossless factorization problem for a generalized state-space system whose transfer matrix is completely general is investigated. The main novelty is that we remove all restrictive hypotheses and allow for arbitrary normal rank, poles and zeros on the imaginary axis, or at infinity. The numerically-sound formulas for the solution bear the same nice expressions and striking simplicity of the inner-outer factorization and may be equally well applied for the (J,J')-spectral factorization.