Many extensions of the standard model of particle physics suggest that neutrinos should be Majorana-type fermions-that is, that neutrinos are their own anti-particles-but this assumption is difficult to confirm. Observation of neutrinoless double-β decay (0νββ), a spontaneous transition that may occur in several candidate nuclei, would verify the Majorana nature of the neutrino and constrain the absolute scale of the neutrino mass spectrum. Recent searches carried out with (76)Ge (the GERDA experiment) and (136)Xe (the KamLAND-Zen and EXO (Enriched Xenon Observatory)-200 experiments) have established the lifetime of this decay to be longer than 10(25) years, corresponding to a limit on the neutrino mass of 0.2-0.4 electronvolts. Here we report new results from EXO-200 based on a large (136)Xe exposure that represents an almost fourfold increase from our earlier published data sets. We have improved the detector resolution and revised the data analysis. The half-life sensitivity we obtain is 1.9 × 10(25) years, an improvement by a factor of 2.7 on previous EXO-200 results. We find no statistically significant evidence for 0νββ decay and set a half-life limit of 1.1 × 10(25) years at the 90 per cent confidence level. The high sensitivity holds promise for further running of the EXO-200 detector and future 0νββ decay searches with an improved Xe-based experiment, nEXO.