Results from a search for neutrinoless double-beta decay (0 nu beta beta) of Xe-136 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 twofold to 3.7 x 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 x 10(25) yr at the 90% confidence level.