  We measure the hadronic branching ratios of the Z0 boson into heavy quarks:
Rb=Gamma(Z0->bb)/Gamma(Z0->hadrons) and Rc=Gamma(Z0->cc/Gamma(Z0->hadrons)
using a multi-tag technique. The measurement was performed using about 400,000
hadronic Z0 events recorded in the SLD experiment at SLAC between 1996 and
1998. The small and stable SLC beam spot and the CCD-based vertex detector were
used to reconstruct bottom and charm hadron decay vertices with high efficiency
and purity, which enables us to measure most efficiencies from data. We obtain,
Rb=0.21604 +- 0.00098(stat.) +- 0.00073(syst.) -+ 0.00012(Rc) and, Rc= 0.1744
+- 0.0031(stat.) +- 0.0020(syst.) -+ 0.0006(Rb)
