  In the light of refined and large reactor mixing angle $\theta_{13}$, we have
revisited the texture three and two zero neutrino mass matrices in the flavor
basis. For Majorana neutrinos, it has been explicitly shown that all the
texture three zero mass matrices remain ruled out. Further, for both normal and
inverted mass ordering, for the texture two zero neutrino mass matrices one
finds interesting constraints on the Dirac-like CP violating phase $\delta$ and
Majorana phases $\rho$ and $\sigma$.
