  We complete the proof of Weinberg's no-go theorem on the cosmological
constant problem in classical gravity when the theory has a (global) scale
symmetry. Stimulated with this proof, we explore a solution to the cosmological
constant problem by the help of renormalization group equations. We find that
the manifestly scale invariant regularization method provides a physically
plausible solution to the cosmological constant problem, in particular, to the
issue of radiative instability of the cosmological constant.
