  We consider compact K\"ahlerian manifolds $X$ of even dimension 4 or more,
endowed with a log-symplectic structure $\Phi$, a generically nondegenerate
closed 2-form with simple poles on a divisor $D$ with local normal crossings. A
simple linear inequality involving the iterated Poincar\'e residues of $\Phi$
at components of the double locus of $D$ ensures that the pair $(X, \Phi)$ has
unobstructed deformations and that $D$ deforms locally trivially.
