  The consequences of a texture zero at the $ee$ entry of neutrino mass matrix
in the flavor basis, which also implies a vanishing effective Majorana mass for
neutrinoless double beta decay, have been studied for Majorana neutrinos. The
neutrino parameter space under this condition has been constrained in the light
of all available neutrino data including the CHOOZ bound on $s_{13}^{2}$.
