  If $R$ is a commutative ring, $I$ an ideal of $R$ and $v, w \in Um_{2n}(R,
I)$ then we show that $v, w$ are in the same orbit of elementary action if and
only if they are in the same orbit of elementary symplectic action. We also
show that if $A$ is a non-singular affine algebra of dimension $d$ over an
algebraically closed field $k$ such that $d! A = A$, $d \equiv 2 \pmod 4$ and
$I$ an ideal of $A$, then $Um_d(A, I) = e_1{Sp}_d(A, I)$. As a consequence it
is proved that if $A$ is a non-singular affine algebra of dimension $d$ over an
algebraically closed field $k$ such that $(d + 1)!A = A$, $d \equiv 1 \pmod 4$
and $I$ a principal ideal then $Sp_{d-1}(A, I) \cap {ESp}_{d+1}(A, I) =
{ESp}_{d -1}(A, I)$. We give an example to show that the above result does not
hold true for an affine algebra over a $C_2$ field and also show by an example
that the above stability estimate is optimal.
