  We investigate a new identity for Green functions using the higher covariant
derivative regularization. It relates some coefficients in the vertex function
of the matter superfield, in which one of external matter lines is not chiral.
The calculation in the first nontrivial order (for the two-loop vertex
function) reveals that the new identity is also valid for the non-Abelian
Yang--Mills theory with matter fields. The new identity is shown to appear
because three-loop integrals, defining the Gell-Mann--Low function are
factorized into integrals of total derivatives.
