We report on an improved measurement of the 2 u beta beta half-life of Xe-136 performed by EXO-200. The use of a large and homogeneous time projection chamber allows for the precise estimate of the fiducial mass used for the measurement, resulting in a small systematic uncertainty. We also discuss in detail the data analysis methods used for double-beta decay searches with EXO-200, while emphasizing those directly related to the present measurement. The Xe-136 2 u beta beta half-life is found to be 2.165 +- 0.016 (stat) +- 0.059 (sys) x 10^21 years. This is the most precisely measured half-life of any 2 u beta beta decay to date.
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