  We propose a method to solve the Non Perturbative Renormalization Group
equations for the $n$-point functions. In leading order, it consists in solving
the equations obtained by closing the infinite hierarchy of equations for the
$n$-point functions. This is achieved: i) by exploiting the decoupling of modes
and the analyticity of the $n$-point functions at small momenta: this allows us
to neglect some momentum dependence of the vertices entering the flow
equations; ii) by relating vertices at zero momenta to derivatives of lower
order vertices with respect to a constant background field. Although the
approximation is not controlled by a small parameter, its accuracy can be
systematically improved. When it is applied to the O(N) model, its leading
order is exact in the large $N$ limit; in this case, one recovers known results
in a simple and direct way, i.e., without introducing an auxiliary field.
