Textures with two traceless submatrices of the neutrino mass matrix

We propose a new texture for the light neutrino mass matrix. The proposal is based upon imposing a zero-trace condition on the two-by-two submatrices 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 submatrices may be found sufficient to describe the current data. Eight out of 15 independent possible cases are found to be compatible with current data. Numerical and some approximate analytical results are presented.