  A new proof of perturbative renormalizability and infrared finiteness for a
scalar massless theory is obtained from a formulation of renormalized field
theory based on the Wilson renormalization group. The loop expansion of the
renormalized Green functions is deduced from the Polchinski equation of
renormalization group. The resulting Feynman graphs are organized in such a way
that the loop momenta are ordered. It is then possible to analyse their
ultraviolet and infrared behaviours by iterative methods. The necessary
subtractions and the corresponding counterterms are automatically generated in
the process of fixing the physical conditions for the ``relevant'' vertices at
the normalization point. The proof of perturbative renormalizability and
infrared finiteness is simply based on dimensional arguments and does not
require the usual analysis of topological properties of Feynman graphs.
