  It is known that the $\Theta$-correspondence for a finite reductive dual pair
is not one-to-one in general. In this paper, we propose two maximal one-to-one
sub-relations $\underline\theta,\overline\theta$ of the
$\Theta$-correspondences for a finite dual pair of two unitary groups. These
two correspondences are extensions of the analogue of the $\eta$-correspondence
proposed by Gurevich-Howe.
