  We show that the physical N=4 super Yang-Mills theory on a four-sphere with
an arbitrary gauge group receives no instanton contributions, by clarifying the
relation between the hypermultiplet mass and the equivariant parameters of the
mass-deformed theory preserving N=2 supersymmetry. The correct relation also
implies that N=4 superconformal Yang-Mills theory with gauge group SU(2)
corresponds to Liouville theory on a torus with the insertion of a non-trivial
operator, rather than the identity as have been claimed in the literature.
