Copulas provide a key ingredient in the field of quantitative risk management because of their flexibility upon investigating dependence relations among random variables. Except for several examples, however, copulas are mainly concerned with the static problems, not with the time-dependent situations. In this paper, on the other hand, we deal with the evolution of copulas in discrete processes with multivariate cases, which extend our previous results on the time evolution of copulas and are expected to enhance the applicability of one method to financial mathematics.