  The usual Bogolyubov R-operation works in non-renormalizable theories in the
same way as in renormalizable ones. However, in the non-renormalizable case,
the counter-terms eliminating ultraviolet divergences do not repeat the
structure of the original Lagrangian but contain new terms with a higher degree
of fields and derivatives increasing from order to order of PT. If one does not
aim to obtain finite off-shell Green functions but limits oneself only to the
finiteness of the S-matrix, then one can use the equations of motion and
drastically reduce the number of independent counter-terms. For example, it is
possible to reduce all counter-terms to a form containing only operators with
four fields and an arbitrary number of derivatives. And although there will
still be infinitely many such counter-terms, in order to fix the arbitrariness
of the subtraction procedure, one can normalize the on-shell 4-point amplitude,
which must be known for arbitrary kinematics, plus the 6-point amplitude at one
point. All other multiparticle amplitudes will be calculated unambiguously.
Within the framework of perturbation theory, the number of independent
counter-terms in a given order is limited, so does the number of normalization
conditions. The constructed counter-terms are not absorbed into the
normalization of a single coupling constant, the Lagrangian contains an
infinite number of terms, but after fixing the arbitrariness, it allows one to
obtain unambiguous predictions for observables.
