  We analyze neutrino mass matrices having one texture zero, assuming that the
neutrino mixing matrix has either its first (TM$_1$) or second (TM$_2$) column
identical to that of the tribimaximal mixing matrix. We found that all the six
possible one texture zero neutrino mass matrices are compatible with the
present neutrino oscillation data when combined with TM$_1$ or TM$_2$ mixing.
These textures have interesting predictions for the presently unknown
parameters such as the effective Majorana neutrino mass, the Dirac CP violating
phase and the neutrino mass scale. We also present a way to theoretically
realize some of these textures using $A_4$ symmetry within the framework of
type-I+II seesaw mechanism.
