  We present the results of observations of the $\lambda 3130.4$ \AA
interstellar absorption line of Be II in the direction of zeta Per. The data
were obtained at the Canada-France-Hawaii 3.6m Telescope using the Coud\'e f/4
Gecko spectrograph at a resolving power $\simeq 1.1 \times 10^5$, and a
signal-to-noise ratio S/N $\simeq$ 2000. The Be II line is not detected, and we
obtain an upper limit on the equivalent width $W_{3130.4}\leq30$ $\mu$\AA. This
upper limit is 7 times below the lowest upper limit ever reported hitherto. The
derived interstellar abundance is ($^9$Be/H) $\leq 7 \times 10^{-13}$, not
corrected for the depletion of Be onto interstellar grains; it corresponds to
an upper limit $\delta_{Be} \leq -1.5$ dex on the depletion factor of Be. As
such, it argues in favour of models of formation of dust grains in stellar
atmospheres.
