  In this paper we establish an asymptotic formula for the number of rational
points of bounded anticanonical height which lie on a certain Zariski dense
subset of the biprojective hypersurface \begin{align*} x_1y_1^2+...+x_sy_s^2 =
0 \end{align*} in $\mathbb{P}^{s-1} \times \mathbb{P}^{s-1} $ with $s \geq 7$.
This confirms the Manin conjecture for this variety.
