  In this paper we consider the operator system $\cl{S}_n$ generated by $n$
Cuntz isometries, i.e. the span of the generators of the Cuntz algebra
$\cl{O}_n$ together with their adjoints and the identity. We define an operator
subsystem $\cl{E}_n\subseteq M_{n+1}$ and then prove that $\cl{S}_n$ is
completely order isomorphic to a quotient of $\cl{E}_n$. This result implies a
characterization of positive elements in $M_p(\cl{S}_n)$.
