  By assuming the existence of (quasi)-linear Regge trajectories for heavy
quarkonia in the low energy region, we derive a new, sixth power, meson mass
relation which shows good agreement with experiment for both charmed and beauty
mesons. This relation may be reduced to a quadratic Gell-Mann-Okubo type
formula by fitting the values of the Regge slopes of these (quasi)-linear
trajectories. For charmed mesons, such a formula holds with an accuracy of
$\sim 1$%, and is in qualitative agreement with the relation obtained
previously by the application of the linear spectrum to a meson hexadecuplet.
