  We present a multiloop flow equation for the four-point vertex in the
functional renormalization group (fRG) framework. The multiloop flow consists
of successive one-loop calculations and sums up all parquet diagrams to
arbitrary order. This provides substantial improvement of fRG computations for
the four-point vertex and, consequently, the self-energy. Using the X-ray-edge
singularity as an example, we show that solving the multiloop fRG flow is
equivalent to solving the (first-order) parquet equations and illustrate this
with numerical results.
