  From about 4 million hadronic Z decays recorded by the OPAL detector on and
near to the Z resonance, we select a sample of more than 570000 inclusively
reconstructed B mesons. Orbitally-excited mesons B*J are reconstructed using
Bpi+- combinations. Independently, B* mesons are reconstructed using the decay
B* -> Bgamma. The selected B* candidates are used to obtain samples enriched or
depleted in the decay B*J -> B*pi+-(X), where (X) refers to decay modes with or
without additional accompanying decay particles. From the number of signal
candidates in the Bpi+- mass spectra of these two samples, we perform the first
measurement of the branching ratio of orbitally-excited B mesons decaying into
B*pi(X):
  BR(B*J ->B*pi(X)) = 0.85 +0.36-0.37 +- 0.12, where the first error is
statistical and the second systematic. If B*J decay modes other than single
pion transitions can be neglected the measured ratio corresponds to the
branching ratio BR(B*J->B*pi). In the framework of Heavy Quark Symmetry, a
simultaneous fit to the Bpi+- mass spectra of the samples enriched or depleted
in B*J->B*pi+-(X) decays yields the mass and the width of the B1(3/2) state, as
well as the branching ratio of B*J mesons decaying into B*pi: M(B1(3/2)) =
(5.738 +0.005-0.006 +-0.007) GeV/c2 G(B1(3/2)) = (18 +15-13 +29-23) MeV/c
BR(B*J->B*pi) = 0.74 +0.12-0.10 +0.21-0.15, where the uncertainties are
statistical and systematic, respectively.
