The (J, J’)-lossless factorization plays an important role in H-infinity control theory, just like the Wiener-Hopf factorization does in LQG theory, for continuous-time systems. In this paper, the theory of J-lossless factorization is extended to discrete-time systems. The notion of J-lossless conjugation, which is a powerful tool for computing J-lossless factorization in continuous-time systems, is also extended to discrete-time systems. These extensions are far from trivial. The discrete-time version of J-lossless conjugations and factorizations turns out to be much more complicated, reflecting the complicated nature of the discrete-time Riccati equations.