$R^*$ operation in the minimal subtraction scheme

The formalism of the $R^*$ operation [1] is developed; it generalizes the $R$ operation and eliminates both ultraviolet and infrared divergences. By explicit formulation of the concept of an infrared counterterm it is shown that the calculation of an arbitrary $(\Re+1)$-loop ultraviolet or infrared eounterterm in the minimal subtraction scheme can be reduced to the finding of the divergent and finite parts of certain massless Feynman integrals that depend only on a single external momentum with number of loops not exceeding $\Re$.