  In the paper we study the Yang-Mills effective action in the four-dimensional
space-time by using background field formalism. We give an explicit way of
cutoff regularization procedure, then do a two-loop renormalization and
calculate a second $\beta$-function coefficient. We also show that the two-loop
singularity contains only logarithmic part in the first degree. At the same
time additional properties of a Green function regular part are obtained.
