We prove that for an embedded unstable one-sided minimal hypersurface of the |$(n+1)$| -dimensional real projective space, the Morse index is at least |$n+2$| , and this bound is attained by the cubic isoparametric minimal hypersurfaces. We also show that there exist closed embedded two-sided minimal surfaces in the 3-dimensional real projective space of each odd index by computing the index of the Lawson surfaces.