The most accurate value of the negative-muon magnetic moment, mu(mu-)
=3.183345(10)mu(p), is Obtained by combining the negative-muon mass fr
om x-ray transitions in muonic atoms and the reanalyzed negative-muon
g factor with the proton magnetic moment in Bohr magnetons. The fracti
onal uncertainty of 3.1X10(-6) is 15 times more accurate than any prev
ious direct measurement. The obtained ratio of the magnetic moments of
the positive muon and the negative muon, mu(mu+) /mu(mu-) = 1.0000002
(31), provides a test of CPT invariance alt the level of 3 ppm. The ne
gative-muon g factor g(mu-) and the magnetic moment anomaly derived fo
r a(mu-) derived for a test of CPT theorem are obtained from an approa
ch now made possible using the new value of the negative-muon magnetic
moment. To substantially improve the verification of the CPT theorem
for the muon g factor, a much more precise value for mu(mu-)/mu(p) is
needed to determine the anomalous g factor a(mu-) for the new Brookhav
en National Laboratory muon g-2 experiment.