  We adapt the precise definition of the flowing effective action in order to
obtain a functional flow equation with simple properties close to physical
intuition. The simplified flow equation is invariant under local gauge
transformations and suitable for both euclidean and Minkowski signature and
analytic continuation. The cutoff always removes fluctuations close to zeros of
the inverse full propagator. A formulation of the simplified flow equation in
terms of renormalized scale invariant fields permits direct access to scaling
solutions and associated fixed points. Corrections to the simplified flow
equation involve a field-dependent modification of the cutoff for which we
discuss a systematic expansion. Truncated solutions for a scalar field theory
in four dimensions suggest a new fixed point with a field-dependent coefficient
of the kinetic term.
