  We combine two non-perturbative approaches, one based on the
two-particle-irreducible (2PI) action, the other on the functional
renormalization group (fRG), in an effort to develop new non-perturbative
approximations for the field theoretical description of strongly coupled
systems. In particular, we exploit the exact 2PI relations between the
two-point and four-point functions in order to truncate the infinite hierarchy
of equations of the functional renormalization group. The truncation is "exact"
in two ways. First, the solution of the resulting flow equation is independent
of the choice of the regulator. Second, this solution coincides with that of
the 2PI equations for the two-point and the four-point functions, for any
selection of two-skeleton diagrams characterizing a so-called $\Phi$-derivable
approximation. The transformation of the equations of the 2PI formalism into
flow equations offers new ways to solve these equations in practice, and
provides new insight on certain aspects of their renormalization. It also opens
the possibility to develop approximation schemes going beyond the strict
$\Phi$-derivable ones, as well as new truncation schemes for the fRG hierarchy.
