  We show that the application of Regge phenomenology to SU(4) meson multiplets
leads to a new Gell-Mann-Okubo mass-mixing formula in the SU(3) sector, 3m_1^2
+ (cos theta)^2 m_0^2 + (sin theta)^2 m_{0'}^2 + sqrt{2} sin(2theta) (m_0^2 -
m_{0'}^2) = 4m_{1/2}^2, where m_1,m_{1/2},m_0,m_{0'} are the masses of the
isovector, isodoublet, isoscalar mostly octet and isoscalar mostly singlet
states, respectively, and theta is the nonet mixing angle. For an ideally mixed
nonet, theta = arctan(1/sqrt{2}), this formula reduces to 2m_0^2 + 3m_1^2 =
4m_{1/2}^2 + m_{0'}^2 which holds with an accuracy of ~1% for vector and tensor
mesons. For pseudoscalar mesons, with the eta-eta' mixing angle
-arctan[1/(2sqrt{2})] ~ -19.5^o, in agreement with experiment, it leads to the
relation 4m_K^2 = 3m_pi^2 + m_{eta'}^2 which holds to an accuracy of better
than 1% for the measured pseudoscalar meson masses.
