  For a smooth affine algebra $R$ of dimension $d \geq 3$ over a field $k$ and
an invertible alternating matrix $\chi$ of rank $2n$, the group $Sp(\chi)$ of
invertible matrices of rank $2n$ over $R$ which are symplectic with respect to
$\chi$ acts on the right on the set $Um_{2n}(R)$ of unimodular rows of length
$2n$ over $R$. In this paper, we prove that $Sp(\chi)$ acts transitively on
$Um_{2n}(R)$ if $k$ is algebraically closed, $d! \in k^{\times}$ and $2n \geq
d$.
