  We rederive non-perturbatively the Coleman-Weinberg expression for the
effective potential for massless scalar QED. Our result is not restricted to
small values of the coupling constants. This shows that the Coleman- Weinberg
result can be established beyond the range of validity of perturbation theory.
Also, we derive it in a manifestly renormalization group invariant way. It is
shown that with the derivation given no Landau ghost singularity arises. The
finite temperature case is discussed.
  Pacs number: 11.10.Ef,11.10.Gh.
