  By assuming the existence of (quasi)-linear Regge trajectories for heavy
mesons, we derive new quadratic mass relations of non-Gell-Mann-Okubo type,
6M^2(q-qbar)+3M^2(c-cbar)=8M^2(c-qbar), 20M^2(q-qbar)+5M^2(b-bbar)=
16M^2(b-qbar), q=n(=u,d),s, which show excellent agreement with experiment. We
also establish the sum rule M^2(i-ibar)+M^2(j-jbar)-2M^2(j-ibar)\approx const
for any pair of flavors, (i,j).
