  We discuss the $\{ \beta \}$-expansion for renormalization group invariant
quantities tracing this expansion to the different contractions of the
corresponding incomplete BPHZ $R$-operation. All of the coupling
renormalizations, which follow from these contractions, should be taken into
account for the $\{ \beta \}$-expansion. We illustrate this feature considering
the nonsinglet Adler function $D^\text{NS}$ in the third order of perturbation.
We propose a generalization of the $\{ \beta \}$-expansion for the
renormalization group covariant quantities -- the $\{ \beta,\gamma
\}$-expansion.
