  Let $P$ be a polarization on a symplectic manifold for which there exists a
metalinear frame bundle. We show that for any other compatible polarization
$P'$ there exists a unique metalinear frame bundle such that the BKS-pairing is
well defined. This means that we do not need the metaplectic frame bundle (nor
a positivity condition on $P$) to achieve this goal, and thus the name
"metaplectic correction" is inappropriate.
