Improvement of the fine-structure constant obtained from the electron g-2

At present the most precise value of the fine-structure constant is /spl alpha/(a/sub e/) obtained from the anomalous magnetic moment of the electron, or the electron g-2. Further improvement in the theoretical calculation of /spl alpha/(a/sub e/) requires reduction of both statistical and nonstatistical uncertainties in the Monte-Carlo evaluation of the /spl alpha//sup 4/ term. This paper analyzes some inconsistency of earlier results and identifies its source as a deviation of nonstatistical nature caused by round-off errors. This information enables us to greatly improve the statistical basis of the electron g-2 value to very high statistics while minimizing the uncertainty of the nonstatistical type. This work will lead to a value of /spl alpha/(a/sub e/) with a relative uncertainty of less than 10/sup -9/ when new measurements become available.