  In view of the latest T2K and MINOS neutrino oscillation data which hint at a
relatively large theta_13, we perform a systematic study of the Majorana
neutrino mass matrix M_nu with two independent texture zeros. We show that
three neutrino masses (m_1, m_2, m_3) and three CP-violating phases (delta,
rho, sigma) can fully be determined from two neutrino mass-squared differences
(delta m^2, Delta m^2) and three flavor mixing angles (theta_12, theta_23,
theta_13). We find that seven patterns of M_nu (i.e., A_{1,2}, B_{1,2,3,4} and
C) are compatible with current experimental data at the 3-sigma level, but the
parameter space of each pattern is more strictly constrained than before. We
demonstrate that the texture zeros of M_nu are stable against the one-loop
quantum corrections, and there exists a permutation symmetry between Patterns
A_1 and A_2, B_1 and B_2 or B_3 and B_4. Phenomenological implications of M_nu
on the neutrinoless double-beta decay and leptonic CP violation are discussed,
and a realization of those texture zeros by means of the Z_n flavor symmetries
is illustrated.
