  An analytical approach is carried out that provides an inviscid stability
criterion for the strato-rotational instability (in short SRI) occurring in a
Taylor-Couette system. The control parameters of the problem are the rotation
ratio $\mu$ and the radius ratio $\eta$. The study is motivated by recent
experimental \cite{legal} and numerical \cite{rudi, rudi2} results reporting
the existence of unstable modes beyond the Rayleigh line for centrifugal
instability ($\mu =\eta^2$). The modified Rayleigh criterion for stably
stratified flows provides the instability condition, $\mu<1$, while in
experiments unstable modes were never found beyond the line $\mu=\eta$. Taking
into account finite gap effects, we consider non axisymmetric perturbations
with azimuthal wavenumber $l$ in the limit $l Fr<<1$, where $Fr$ is the Froude
number. We derive a necessary condition for instability : $\mu < \mu^*$ where
$\mu^*$, a function of $\eta$, takes the asymptotic values, $\mu^* \to 1$ in
the narrow gap limit, and $\mu^* \to 2\eta^2(1+\eta)$ in the wide gap limit, in
agreement with recent numerical findings. A stronger condition, $\mu<\eta$, is
found when $\eta>0.38$, in agreement with experimental results obtained for
$\eta=0.8$. Whatever the gap size, instability is predicted for values of $\mu$
larger than the critical one, $\mu_c=\eta^2$, corresponding to centrifugal
instability.
