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