  The renormalization procedure is proved to be a rigorous way to get finite
answers in a renormalizable class of field theories. We claim, however, that it
is redundant if one reduces the requirement of finiteness to S-matrix elements
only and does not require finiteness of intermediate quantities like the
off-shell Green functions. We suggest a novel view on the renormalization
procedure. It is based on the usual BPHZ R-operation, which is equally
applicable to any local QFT, renormalizable or not. The key point is the
replacement of the multiplicative renormalization, used in renormalizable
theories, by an operation when the renormalization constants depend on the
fields and momenta that have to be integrated inside the subgraphs. This
approach does not distinguish between renormalizable and non-renormalizable
interactions and provides the basis for getting finite scattering amplitudes in
both cases. The arbitrariness of the subtraction procedure is fixed by imposing
a normalization condition on the scattering amplitude as a whole rather than on
an infinite series of new operators appearing in non-renormalizable theories.
  Using the property of locality of counter-terms, we get recurrence relations
connecting leading, subleading, etc., UV divergences in all orders of PT in any
local theory. This allows one to get generalized RG equations that have an
integro-differential form and sum up the leading logarithms. This way one can
cure the problem of violation of unitarity in non-renormalizable theories by
summing up the leading asymptotics. We illustrate the basic features of our
approach by several examples.
  Our main statement is that non-renormalizable theories are self-consistent,
they can be well treated within the usual BPHZ R-operation, and the
arbitrariness can be fixed to a finite number of parameters just as in the
renormalizable case.
