Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)The mass dimension one fermionic field associated with Elko satisfies the Klein-Gordon but not the Dirac equation. However, its propagator is not a Green's function of the Klein-Gordon operator. We propose an infinitesimal deformation to the propagator such that it admits an operator in which the deformed propagator is a Green's function. The field is still of mass dimension one, but the resulting Lagrangian is modified in accordance with the operator. (C) 2016 The Author. Published by Elsevier B.V.760164169CNPq [313285/2013-6]Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)