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Results from a search for neutrinoless double-beta decay (0νββ) 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 σ/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 0νββ and background events have been developed. Incorporating these hardware and analysis improvements, the median 90% confidence level 0νββ half-life sensitivity after combining with the full data set acquired before the upgrade has increased twofold to 3.7×10^{25}  yr. No statistically significant evidence for 0νββ is observed, leading to a lower limit on the 0νββ half-life of 1.8×10^{25}  yr at the 90% confidence level.

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