  A nonperturbative method is proposed for the approximative solution of the
exact evolution equation which describes the scale dependence of the effective
average action. It consists of a combination of exact evolution equations for
independent couplings with renormalization group improved one loop expressions
of secondary couplings. Our method is illustrated by an example: We compute the
beta-function of the quartic coupling lambda of an O(N) symmetric scalar field
theory to order lambda^3 as well as the anomalous dimension to order lambda^2
using only one loop expressions and find agreement with the two loop
perturbation theory. We also treat the case of very strong coupling and confirm
the existence of a "triviality bound".
