Results from a search for neutrinoless double-beta decay $0 ubetabeta$ 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 $0 ubetabeta$ and background events have been developed. Incorporating these hardware and analysis improvements, the median 90% confidence level $0 ubetabeta$ 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 $0 ubetabeta$ is observed, leading to a lower limit on the $0 ubetabeta$ half-life of $1.8times10^{25}$ yr at the 90% confidence level.
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