We revisit the study of the maximally singular point in the Coulomb branch of
4d N=2 SU(N) gauge theory with N_f=2n flavors for N_f<2N. When n >= 2, we find
that the low-energy physics is described by two non-trivial superconformal
field theories coupled to a magnetic SU(2) gauge group which is infrared free.
(In the special case n=2, one of these theories is a theory of free
hypermultiplets.) This observation removes a possible counter example to a
conjectured a-theorem.