The fraction of Z0→bb¯¯¯Z0→bb¯ events in hadronic Z0Z0 decays has been measured by the OPAL experiment using the data collected at LEP between 1992 and 1995. The Z0→bb¯¯¯Z0→bb¯ decays were tagged using displaced secondary vertices, and high momentum electrons and muons. Systematic uncertainties were reduced by measuring the b-tagging efficiency using a double tagging technique. Efficiency correlations between opposite hemispheres of an event are small, and are well understood through comparisons between real and simulated data samples. A value of was obtained, where the first error is statistical and the second systematic. The uncertainty on RcRc , the fraction of Z0→cc¯¯Z0→cc¯ events in hadronic Z0Z0 decays, is not included in the errors. The dependence on RcRc is where $\Delta R_{\rm c}$ is the deviation of RcRc from the value 0.172 predicted by the Standard Model. The result for RbRb agrees with the value of 0.2155±0.00030.2155±0.0003 predicted by the Standard Model.