  We propose a new texture for the light neutrino mass matrix. The proposal is
based upon imposing zero-trace condition on the two by two sub-matrices of the
complex symmetric Majorana mass matrix in the flavor basis where the charged
lepton mass matrix is diagonal. Restricting the mass matrix to have two
traceless sub-matrices may be found sufficient to describe the current data.
Eight out of fifteen independent possible cases are found to be compatible with
current data. Numerical and some approximate analytical results are presented.
