Necessary and sufficient conditions for a class of dissipative nonlinear multi-input multi-output discrete-time systems are given. The conditions existing in the literature, addressed as Kalman-Yakubovich-Popov conditions, for the dissipative, passive or lossless cases, are derived from the proposed dissipativity characterization. Feedback passivity is solved for a class of multi-input multi-output nonlinear discrete-time systems affine in the control input using the properties of the relative degree and zero dynamics of the non-passive system. This is the first solution presented in the literature to such a problem in the discrete-time setting. The passification methodology is illustrated by means of an example.