  Let $\mathcal{F}_1(n,m)$ be the space of ordered m-tuples of pairwise
distinct points in $\partial \mathbf{H}_{\mathbb{H}}^n$ up to its isometry
group $PSp(n,1)$. It is a real $2m^2-6m+5-\sum^{m-n-1}_{i=1}{m-2 \choose
n-1+i}$ dimensional algebraic variety when $m>n+1$. In this paper, we construct
and describe the moduli space of $\mathcal{F}_1(n,m)$, in terms of the Cartan's
angle and cross-ratio invariants, by applying the Moore's determinant.
