  The latest data from Planck collaboration has presented an improved
sensitivity limit of the sum of neutrino masses ($\Sigma$), $\Sigma <0.17eV$ at
95$\%$ confidence level (CL). On the other hand, the updated global fits of
neutrino oscillation have shown a refined range of atmospheric mixing angle
$\theta_{23}$ at the same CL. In the light of these observations, we have
re-investigated the five viable cases ( $B_{1, 2, 3, 4}$ and $C$) of texture
two zero Majorana mass matrix in the flavor basis. Using the present Planck's
data, we have demonstrated that only cases $B_{2}$ and $B_{4}$ are now viable
for normal mass ordering, while remaining three cases does not meet the present
experimental constraints at 2$\sigma$ CL. The viable cases are also found to be
in agreement with the latest T2K, Super-Kamiokande and NO$\nu$A results,
indicating the preference for normal neutrino mass ordering ($m_{1} <
m_{2}<m_{3}$), a maximal Dirac CP-violating phase ($\delta \simeq 270^{0}$),
and upper octant of neutrino mixing angle ($\theta_{23} > 45^{0}$). In
addition, the implication of $\Sigma$ on neutrinoless double beta decay is
studied for viable cases.
