  Results from a search for neutrinoless double-beta decay $0\nu\beta\beta$ of
$^{136}$Xe are presented using the first year of data taken with the upgraded
EXO-200 detector. Relative to previous searches by EXO-200, the energy
resolution of the detector has been improved to $\sigma/E$=1.23%, the electric
field in the drift region has been raised by 50%, and a system to suppress
radon in the volume between the cryostat and lead shielding has been
implemented. In addition, analysis techniques that improve topological
discrimination between $0\nu\beta\beta$ and background events have been
developed. Incorporating these hardware and analysis improvements, the median
90% confidence level $0\nu\beta\beta$ half-life sensitivity after combining
with the full data set acquired before the upgrade has increased 2-fold to $3.7
\times 10^{25}$ yr. No statistically significant evidence for $0\nu\beta\beta$
is observed, leading to a lower limit on the $0\nu\beta\beta$ half-life of
$1.8\times10^{25}$ yr at the 90% confidence level.
