  In this note we prove a non-renormalization theorem for the 3-point functions
of 1/2 BPS primaries in the four-dimensional N = 4 SYM and chiral primaries in
two dimensional N =(4,4) SCFTs. Our proof is rather elementary: it is based on
Ward identities and the structure of the short multiplets of the superconformal
algebra and it does not rely on superspace techniques. We also discuss some
possible generalizations to less supersymmetric multiplets.
