  We study a Shimura variety attached to a unitary similitude group of a
skew-Hermitian form over a totally indefinite quaternion algebra over a totally
real number field. We give a necessary and sufficient condition for the
existence of skew-Hermitian self-dual lattices. Under this condition we show
that the superspecial locus in the fiber at $p$ of the associated Shimura
variety is non-empty. We also give an explicit formula for the number of
irreducible components of the supersingular locus when $p$ is odd and
unramified in the quaternion algebra.
