  We show that, in addition to SO(4), the Hubbard model at half filling on a
bipartite lattice has a group of discrete symmetries and transformations. A
unique Hubbard-Stratonovich decomposition of the interaction term,
incorporating both spin and pseudospin variables on an equal footing, is found
in which these symmetries are manifestly present. The consequences of this at
the mean field and one loop renormalisation group levels are discussed.
