A measurement of the forward--backward asymmetry of e+e−→cc¯ and e+e−→bb¯ on the Z resonance is performed using about 3.5 million hadronic Z decays collected by the DELPHI detector at LEP in the years 1992 to 1995. The heavy quark is tagged by the exclusive reconstruction of several D meson decay modes. The forward--backward asymmetries for c and b quarks at the Z resonance are determined to be: \renewcommand{\arraystretch}{1.6} \begin{array}{rcr@{}l} \Afbc(\sqrt{s} = 91.235 {\rm GeV}) &=& &#;0659 \pm 0.0094 (stat) \pm 0.0035 (syst) \Afbb (\sqrt{s} = 91.235 {\rm GeV}) &=& &#;0762 \pm 0.0194 (stat) \pm 0.0085 (syst) \Afbc(\sqrt{s} = 89.434 {\rm GeV}) &=&-&#;0496 \pm 0.0368 (stat) \pm 0.0053 (syst) \Afbb(\sqrt{s} = 89.434 {\rm GeV}) &=& &#;0567 \pm 0.0756 (stat) \pm 0.0117 (syst) \Afbc(\sqrt{s} = 92.990 {\rm GeV}) &=& &#;1180 \pm 0.0318 (stat) \pm 0.0062 (syst) \Afbb(\sqrt{s} = 92.990 {\rm GeV}) &=& &#;0882 \pm 0.0633 (stat) \pm 0.0122 (syst) \end{array}