  We give another proof of an observation of Th\'evenaz \cite{T1989} and
present a fusion system version of it. Namely, for a saturated fusion system
$\CF$ on a finite $p$-group $S$, we show that the number of the $\CF$-conjugacy
classes of cyclic subgroups of $S$ is equal to the rank of certain square
matrices of numbers of orbits, coming from characteristic bisets, the
characteristic idempotent and finite groups realizing the fusion system $\CF$
as in our previous work \cite{P2010}.
