  We discuss the perturbative behavior of the 1/2 BPS operators in N=2 SCFT on
the example of two very similar quadrilinear composite operators made out of
hypermultiplets. An explicit one-loop computation shows that one of them is
protected while the other acquires an anomalous dimension. Although both
operators are superconformal primaries in the free case, the quantum
corrections make the latter become a 1/2 BPS descendant of the Konishi
multiplet, while the former remains primary. The comparative study of these two
operators at higher orders may be helpful in understanding the quantum
properties of the Konishi multiplet.
