  Let $X\to\P^n$ be a $2n$-dimensional projective holomorphic symplectic
manifold admitting a Lagrangian fibration over $\P^n$. Matsushita proved that
the fibration can be deformed in a codimension one family in the moduli space
$\mathrm{Def}(X)$ of deformations of $X$. We extend his result by proving that
if the Lagrangian fibration admits a section, then there is a codimension two
family of deformations which also preserve the section.
