Constraints on Neutrino Mass Matrix with no Majorana Phases

In the basis where charged lepton mass matrix is real and diagonal, we have found conditions under which there are no Majorana phases in neutrino mass matrix. An important feature of the condition is that it has been formulated in terms of modulus of the elements of neutrino mass matrix independent of phases. If these conditions are satisfied, a CKM type matrix is enough to make neutrino Majorana mass matrix real and diagonal without any need of Majorana phases. As an application, we explore the possibility of Majorana phases in all phenomenologically acceptable neutrino mass matrices with two texture zeros.