  We explore the gauge dependence of the effective average action within the
functional renormalization group (FRG) approach. It is shown that in the
framework of standard definitions of FRG for the Yang-Mills theory, the
effective average action remains gauge-dependent on-shell, independent on the
use of truncation scheme. Furthermore, we propose a new formulation of the FRG,
based on the use of composite operators. In this case one can provide on-shell
gauge-invariance for the effective average action and universality of
$S$-matrix.
