In the simple model of neutrino texture presented in this paper, the Majorana lefthanded mass matrix is zero, the Majorana righthanded mass matrix --- diagonal and degenerate, and the Dirac mass matrix has a hierarchical structure, deformed unitarily by nearly bimaximal mixing. In the case, when the Majorana righthanded term dominates over the Dirac term, the familiar seesaw mechanism leads effectively to the nearly bimaximal oscillations of active neutrinos, consistent with solar and atmospheric neutrino experiments. If the Dirac term, before its unitary deformation, is similar in shape to the known charged-lepton mass matrix, then parameters for solar \nu _e's and atmospheric \nu _\mu 's become related to each other, predicting from the SuperKamiokande value of \Delta  m₃₂² a tiny \Delta  m₂₁² typical for MSW LOW solar solution rather than for MSW Large Mixing Angle solution. The predicted mass spectrum is then hierarchical. In Appendix a suggestive form of nearly bimaximal effective mass matrix is derived.

PACS numbers: 12.15.Ff, 14.60.Pq, 12.15.Hh.