The discretization in Method of Moments (MoM) of the Electric-Field Integral Equation (EFIE) is traditionally carried out by preserving the continuity of the normal component in the expansion of the current across the edges arising from the discretization. This allows the cancellation of the hyper-singular Kernel contributions arising from the discretization of the EFIE. Divergence-conforming sets, like the RWG set, appear then as suitable choices to generate successful MoM-EFIE implementations. In this paper, we present a novel MoM- discretization of the EFIE with the non-conforming monopolar- RWG basis functions, with jump discontinuities in the expanded normal component of the current. We show with RCS results that the new EFIE implementation shows good agreement with the traditional normal-continuous RWG-implementation.