Migdal's renormalization group transformation for theSU (N) pure lattice-gauge model is solved in the weak coupling regime by a perturbative expansion in the coupling constant. The heat-kernel model is shown to be a low-order perturbative solution of the Migdal recursion relation. The parameters of the β-function are fixed within theSU (N) Migdal model. The critical coupling constant of the deconfining phase transition is approximately calculated and compared with constants obtained by the heat-kernel model and numerical calculations. The improved actions for theSU (2) andSU (3) are presented for realistic lattice-gauge methods such as the Monte Carlo simulation.