The muon (g - 2) experiment E821 is currently in progress at Brookhaven National Laboratory. Four data-taking runs for positive muons and one run for negative muons were successfully accomplished in 1997-2000 and 2001, respectively. Results of the 1997-2000 runs have been published, thus completing our experiment for μ+. Data analysis for the 2001 run for μ- is currently in progress. To provide measurement of αμ- = 1/2(g - 2)μ- at the same level of accuracy as for αμ+ = 1/2 (g - 2)μ+, we would need one more data-taking run.