From about 4 M hadronic Z decays recorded by OPAL, we select a sample of more than 57000 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. 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. If B*J decay modes other than single pion transitions can be neglected the measured ratio corresponds to 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 BR(B*J->B*pi).