An effective texture is presented for six Majorana conventional neutrinos (three active and three sterile), based on a 6\times 6 neutrino mixing matrix whose 3\times 3 active--active component arises from the popular bimaximal mixing matrix of active neutrinos \nu _e,  \nu _\mu ,  \nu _\tau by three small rotations in the 14, 25, 36 planes of \nu ₁ , \nu ₂  ,  \nu ₃ and  \nu ₄ , \nu₅,  \nu ₆ neutrino mass states. The Dirac component (i.e. , 3 \times 3 active-sterile component) of the resulting 6 \times 6 neutrino mass matrix is conjectured to get a structure similar to the charged-lepton and quark 3 \times 3 mass matrices, after the bimaximal mixing, specific for neutrinos, is transformed out unitarily from the neutrino mass matrix. The charged-lepton and quark mass matrices are taken in a universal form constructed previously by the author with a conside- rable phenomenological success. Then, for the option of m²₁ \simeq m²₂ \simeq m²₃ \gg m²₄ \simeq m²₅ \simeq m²₆ \simeq 0, the proposed texture predicts oscillations of solar \nu _e's with \Delta m²_sol \equiv \Delta m²₂₁ \sim  (1.1 to 1.2) \times 10^-5   eV², not inconsistent with the LMA solar solution, if the SuperKamiokande value \Delta m²_atm \equiv \Delta m²₃₂ \sim  (3 to 3.5) \times 10^-3eV² for oscillations of atmospheric \nu _\mu 's is taken as an input. Here, sin² 2\theta _sol \sim 1 and sin² 2 \theta _atm \sim 1. The texture predicts also an LSND effect with sin² 2\theta _LSND  (1.4 to 1.9)\times 10^-11  (eV/m₁)⁴ and \Delta m²_LSND \equiv \Delta m²₂₅ \sim m²₁ +  (1.1 to 1.2) 10^-5\mskip \thickmuskip {eV}². Unfortunately, the Chooz experiment imposes on the LSND effect (in our texture) a very small upper bound  sin² 2\theta _LSND  \lesssim 1.3 \times 10^-3, which corresponds to the lower limit m₁  \gtsim (1.0 to 1.1)\times 10^-2 eV.

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