Intrinsic reflections in Coxeter systems

Let $(W,S)$ be a Coxeter system and let $s\in S$. We call $s$ a right-angled generator of $(W,S)$ if $st=ts$ or $st$ has infinite order for each $t \in S$\mathrm{.}Wecall$s$anintrinsicreflectionof$W$if$s \in R^W$ for all Coxeter generating sets $R$ of $W$. We give necessary and sufficient conditions for a right-angled generator $s\in S$ of $(W,S)$ to be an intrinsic reflection of $W$.