We present our analysis of the decay constants of the beauty vector mesons B^* and B^*_s within the framework of dispersive sum rules for the two-point correlator of vector currents in QCD. While the decay constants of the vector mesons f_B^* and f_B_s^* - similar to the decay constants of the pseudoscalar mesons f_B and f_B_s - individually have large uncertainties induced by theory parameters not known with a satisfactory precision, these uncertainties almost entirely cancel out in the ratios

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... of vector over pseudoscalar decay constants. These ratios may be thus predicted with very high accuracy due to the good control over the systematic uncertainties of the decay constants gained upon application of our hadron-parameter extraction algorithm. Our final results read f_B^*/f_B=0.944±0.011_ OPE±0.018_ syst and f_B_s^*/f_B_s=0.947±0.023_ OPE±0.020_ syst. Thus, both f_B^*/f_B and f_B_s^*/f_B_s are less than unity at 2.5σ and 2σ level, respectively.