We suggest a simple modification of the maximal mixing scenario (with Sg permutation symmetry) for three light neutrinos. Our neutrino mass matrix has smaller permutation symmetry S-2(nu(mu) reversible arrow nu(e)), and is consistent with all neutrino experiments except the Cl-37 experiment. The resulting mass eigenvalues for three neutrinos are m(1) approximate to (2.55 - 1.27) x 10(-3) eV, m(2,3) approximate to (0.71 - 1.43) eV for Delta m(LSND)(2) = 0.5 - 2.0 eV(2). Then these light neutrinos can account for similar to (2.4 - 4.8)% (6.2 - 12.4%) of the dark matter for h = 0.8 (0.5). Our model predicts the nu(mu) --> nu(tau) oscillation probability in the range sensitive to the future experiments such as CHORUS and NOMAD.