Similar to the method of S.A. Anikin and O.I. Zavialov a modified renormalization procedure is applied to the already renormalized current operator. This allows the derivation of an identity for the coefficient functions of this operator and the proof of new renormalization group equations. These equations are applied to the theory and the electromagnetic form factor of quarks in QCD. In the last case the one-loop approximation gives the leading behaviour exp(- clnln Q2ln Q2) for large euclidean values of the momentum transfer Q2 = - q2 at the external electromagnetic vertex. If the leading logarithmic terms ( g2ln 2Q2) n are extracted from this result, then the behaviour exp(- g2c'ln 2Q2) is obtained. Whereas the first result is modified by contributions from two-loop calculations, the result concerning the leading logarithmic terms does not change.