  We test a candidate for a four-dimensional C-function. This is done by
considering all asymptotically free, vectorlike gauge theories with N_f flavors
and fermions in arbitrary representations of any simple Lie group. Assuming
spontaneous breaking of chiral symmetry in the infrared limit and that the
value of the C-function in this limit is determined by the number of Goldstone
bosons, we find that only in the case of a theory with two colors and fermions
in one single pseudo-real representation of SU(2) the C-theorem seems to be
violated. Conversely, this might also be a sign of new constraints, restricting
the number of flavors consistent with spontaneous chiral symmetry breaking. For
all other groups and representations we find that this candidate C-function
decreases along the renormalization group flow.
