  Let $S$ be a closed orientable hyperbolic surface with Euler
characteristic$\chi$, and let $\lambda_k(S)$ be the $k$-th positive eigenvalue
for the Laplacian on $S$. According to famous result of Otal and Rosas,
$\lambda_{-\chi}>\frac14$. In this article, we prove that if thesystole of $S$
is greater than 3,46, then $\lambda_{-\chi-1}>\frac14$.This inequality is also
true for geometrically finite orientable hyperbolic surfaces without cusps with
the same assumption on the systole.
