  We reconsider the general constraints on the perturbative anomalous
dimensions in conformal invariant QFT and in particular in N=4 SYM with gauge
group SU(N_c). We show that all the perturbative corrections to the anomalous
dimension of a renormalized gauge invariant local operator can be written as
polynomials in its one loop anomalous dimension. In the N=4 SYM theory the
coefficients of these polynomials are rational functions of the number of
colours N_c.
