  Let ${\bf H}_{\mathbb C}^n$ be the $n$-dimensional complex hyperbolic space
and ${\rm SU}(n,1)$ be the (holomorphic) isometry group. An element $g$ in
${\rm SU}(n,1)$ is called loxodromic or hyperbolic if it has exactly two fixed
points on the boundary $\partial {\bf H}_{\mathbb C}^n$. We classify ${\rm
SU}(n,1)$ conjugation orbits of pairs of loxodromic elements in ${\rm
SU}(n,1)$.
