It has been shown that if C is a
commutative connected semi-local ring with involution J then the Witt ring,
W(C,J), of hermitian forms over C is a factor ring of an integral group ring Z[G],
with G a group of exponent two. The purpose of this note is to characterize those
pairs (C,J) whose Witt rings are actually isomorphic to integral group rings
(Theorem 1).