  We claim that if by a choice of the couplings the theory can be made
conformally invariant (vanishing of the beta functions) it is automatically
finite and vice versa. This is demonstrated by explicit example in
supersymmetric gauge theory. The formalism is then applied to the beta deformed
${\cal N}=4$ SYM theory and it is shown that the requirement of conformal
invariance = finiteness can be achieved for any complex parameter of
deformations.
