  Suppose $\phi_3:Sp(1)\rightarrow Sp(2)$ denotes the unique irreducible
$4$-dimensional representation of $Sp(1) = SU(2)$ and consider the two
subgroups $H_1, H_2\subseteq Sp(3)$ with $H_1 =
\{\operatorname{diag}(\phi_3(q_1), q_1): q_1 \in Sp(1)\}$ and $H_2 =
\{\operatorname{diag}(\phi_3(q_2),1):q_2\in Sp(1)\}$. We show that the
biquotient $H_1\backslash Sp(3)/H_2$ admits a quasi-positively curved
Riemannian metric.
