By means of magnetic, specific heat and pyroelectric measurements, we report on magnetic ferroelectricity in the quadruple perovskite NaMn7O12, characterized by a canted antiferromagnetic (AFM) CE structure. Surprisingly, ferroelectricity is concomitant to a dramatic broadening of the magnetic hysteresis loop, well below the AFM ordering temperature. This unconventional behavior shows that the formation of ferroelectric domains is induced by the symmetric exchange interaction in the local scale, e.g. at magnetic domain boundaries or defects. The large electric polarization, P = 0.027µC cm −2 , measured in polycrystalline samples suggests that the above scenario is very promising indeed for the rational design of practical multiferroic materials.