  We resolve the mixing of the scalar operators of naive dimension 4 belonging
to the representation 20' of the SU(4) R-symmetry in N=4 SYM. We compute the
order g^2 corrections to their anomalous dimensions and show the absence of
instantonic contributions thereof. Ratios of the resulting expressions are
irrational numbers, even in the large N limit where, however, we observe the
expected decoupling of double-trace operators from single-trace ones. We
briefly comment on the generalizations of our results required in order to make
contact with the double scaling limit of the theory conjectured to be
holographically dual to type IIB superstring on a pp-wave.
