  We explore the exponential parameterization of the Majorana neutrino mass
matrix texture. In this regard, the elements of the mass matrix are expressed
in terms of their absolute values and arguments. We propose a neutrino mass
matrix texture that highlights four correlations among its elements. The mixing
scheme obtained from the proposed texture is consistent with experimental
observations. In addition, we derive the proposed texture from the $SU(2)_L
\times U(1)_Y \times A_4 \times Z_{10}$ group in the light of the seesaw
mechanism.
