  We report the results of a search for $\nu_{e}$ appearance in a $\nu_{\mu}$
beam in the MINOS long-baseline neutrino experiment. With an improved analysis
and an increased exposure of $8.2\times10^{20}$ protons on the NuMI target at
Fermilab, we find that $2\sin^2(\theta_{23})\sin^2(2\theta_{13})<0.12\ (0.20)$
at 90% confidence level for $\delta\mathord{=}0$ and the normal (inverted)
neutrino mass hierarchy, with a best fit of
$2\sin^2(\theta_{23})\sin^2(2\theta_{13})\,\mathord{=}\,0.041^{+0.047}_{-0.031}\
(0.079^{+0.071}_{-0.053})$. The $\theta_{13}\mathord{=}0$ hypothesis is
disfavored by the MINOS data at the 89% confidence level.
