  Let $M$ be a smooth manifold of dimension $2n$, and let $O_{M}$ be the dense
open subbundle in $\wedge^{2}T^{\ast}M$ of $2$-covectors of maximal rank. The
algebra of $\operatorname*{Diff}M$-invariant smooth functions of first order on
$O_{M}$ is proved to be isomorphic to the algebra of smooth
$Sp(\Omega_{x})$-invariant functions on $\wedge^{3}T_{x}^{\ast}M$, $x$ being a
fixed point in $M$, and $\Omega_{x}$ a fixed element in $(O_{M})_{x}$. The
maximum number of functionally independent invariants is computed.
