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The usual Bogolyubov R-operation works in non-renormalizable theories in thesame way as in renormalizable ones. However, in the non-renormalizable case,the counter-terms eliminating ultraviolet divergences do not repeat thestructure of the original Lagrangian but contain new terms with a higher degreeof fields and derivatives increasing from order to order of PT. If one does notaim to obtain finite off-shell Green functions but limits oneself only to thefiniteness of the S-matrix, then one can use the equations of motion anddrastically reduce the number of independent counter-terms. For example, it ispossible to reduce all counter-terms to a form containing only operators withfour fields and an arbitrary number of derivatives. And although there willstill be infinitely many such counter-terms, in order to fix the arbitrarinessof 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 onepoint. All other multiparticle amplitudes will be calculated unambiguously.Within the framework of perturbation theory, the number of independentcounter-terms in a given order is limited, so does the number of normalizationconditions. The constructed counter-terms are not absorbed into thenormalization of a single coupling constant, the Lagrangian contains aninfinite number of terms, but after fixing the arbitrariness, it allows one toobtain unambiguous predictions for observables.

How one can obtain unambiguous predictions for the S-matrix in non-renormalizable theories