  Two 3x3 matrices playing the role of annihilation and creation operators in
the neutrino-flavor space of nu_e, nu_mu, nu_tau are applied to construct the
off-diagonal part of neutrino effective mass matrix M. The construction leads
to a new relation between two off-diagonal elements M_{e mu} and M_{mu tau} of
M. In the case of tribimaximal neutrino mixing, this relation implies a new
mass sum rule for nu_1, nu_2, nu_3: m_3 = eta m_2 - (eta - 1)m_1. In a
plausible option consistent with the charged-lepton mass spectrum, one gets eta
\equiv (2/3)(4 sqrt{3}+1) = 5.28547. Then, {Delta m^2_{32}}/{Delta m^2_{21}} =
eta^2 -1 = 26.9362 if m_1 = 0, what predicts Delta m^2_{32} \sim 2.2 x 10^{-3}
eV^2 when the input Delta m^2_{21} \sim 8.0 x 10^{-5} eV^2 is used.
