The off-diagonal part of the active-neutrino mass matrix is constructed from two 3\times 3 matrices playing the role of annihilation and creation matrices acting in the neutrino-generation space of \nu 1, \nu 2 , \nu 3. The construction leads to a new relation, M\mu \tau = 4\sqrt {3} Me \mu , which predicts in the case of tribimaximal neutrino mixing that m3 - m1 = \eta (m2 - m1) with \eta = 5.28547. Then, the maximal possible value of {\Delta m232}/{\Delta m221} is equal to \eta 2 -1 = 26.9362 and gives m1 = 0. With the experimental estimate {\Delta m221}\sim 8.0\times 10-5\mskip \thickmuskip {eV}2, this maximal value, if realized, predicts \Delta m232 \sim 2.2\times 10-3\mskip \thickmuskip {eV}2, near to the popular experimental estimation \Delta m232 \sim 2.4\times 10-3\mskip \thickmuskip {eV} 2.
PACS numbers: 12.15.Ff, 14.60.Pq
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