Quadratic feedback linearization is discussed for discrete-time systems, i.e. approximate feedback linearization up to the second order with respect to input and state variables. After introducing in discrete time two equivalence classes, invariant under quadratic static state feedback and diffeomorphism, two canonical quadratic representations are proposed. Then it is shown that any nonlinear discrete-time dynamics, which are controllable in their first approximations, can be linearized up to the second order under dynamic feedback. The results stated here can be considered as the general discrete-time analogues of the continuous-time ones (Kang and Krener 1992).