  It is proved that Epstein's zeta-function $\zeta_{Q}(s)$, related to a
positive definite integral binary quadratic form, has a zero $1/2 + i\gamma$
with $ T \leq \gamma \leq T + T^{{3/7} +\varepsilon} $ for sufficiently large
positive numbers $T$. This is an improvement of the result by M. Jutila and K.
Srinivas (Bull. London Math. Soc. 37 (2005) 45--53).
