  We extend the known consistency conditions on the low-energy theory of
six-dimensional N = 1 supergravity. We review some facts about the theory of
two-form gauge fields and conclude that the charge lattice Gamma for such a
theory has to be self-dual. The Green-Schwarz anomaly cancellation conditions
in the supergravity theory determine a sublattice of Gamma. The condition that
this sublattice can be extended to a self-dual lattice Gamma leads to a strong
constraint on theories that otherwise appear to be self-consistent.
