  We show that, if $X$ is a closed subspace of a Banach space $E$ and $Z$ is a
closed subspace of $E^*$ such that $Z$ is norming for $X$ and $X$ is total over
$Z$ (as well as $X$ is norming for $Z$ and $Z$ is total over $X$), then $X$ and
the pre-annihilator of $Z$ are complemented in $E$ whenever $Z$ is $w^*$-closed
or $X$ is reflexive.
