  We report an improved measurement of the Land\'e g factor of the 5D5/2 state
of singly ionized barium. Measurements were performed on single Doppler-cooled
138Ba+ ions in linear Paul traps using two similar, independent apparatuses.
Transitions between Zeeman sublevels of the 6S1/2 and 5D5/2 states were driven
with two independent, stabilized radio-frequency synthesizers using a dedicated
electrode within each ion trap chamber. State detection within each Zeeman
manifold was achieved with a frequency-stabilized fiber laser operating at 1.76
microns. By calculating the ratio of the two Zeeman splittings, and using the
measured Land\'e g factor of the 6S1/2 state, we find a value of
1.200371(4stat)(6sys) for g of 5D5/2.
