  We give a local normal form for Dirac structures. As a consequence, we show
that the dimensions of the pre-symplectic leaves of a Dirac manifold have the
same parity. We also show that, given a point $m$ of a Dirac manifold $M$,
there is a well-defined transverse Poisson structure to the pre-symplectic leaf
$P$ through $m$. Finally, we describe the neighborhood of a pre-symplectic leaf
in terms of geometric data. This description agrees with that given by Vorobjev
for the Poisson case
