  Motivated by a problem in local differential geometry of Cauchy--Riemann (CR)
structures of hypersurface type, we find a canonical form for pairs consisting
of a nondegenerate Hermitian form and a self-adjoint antilinear operator, or,
equivalently, consisting of a nondegenerate Hermitian form and a symmetric
bilinear form. This generalizes the only previously known results on
simultaneous normalization of such pairs, namely, the results of Benedetti and
Cragnolini (1984) on simultaneous diagonalization of these pairs in the case
where the Hermitian form is positive definite and of Hong and Horn (1986),
where a criterion for simultaneous diagonalization is given.
