  In a {\cal N}=1 superspace setup and using dimensional regularization, we
give a general and simple prescription to compute anomalous dimensions of
composite operators in {\cal N}=4, SU(N) supersymmetric Yang-Mills theory,
perturbatively in the coupling constant g. We show in general that anomalous
dimensions are responsible for the appearance of higher order poles in the
perturbative expansion of the two-point function and that their lowest
contribution can be read directly from the coefficient of the 1/\epsilon^2
pole. As a check of our procedure we rederive the anomalous dimension of the
Konishi superfield at order g^2. We then apply this procedure to the case of
the double trace, dimension 4, superfield in the 20 of SU(4) recently
considered in the literature. We find that its anomalous dimension vanishes for
all N in agreement with previous results.
