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We have investigated the dielectric and magnetic properties of Eu$_{0.595}$Y$_{0.405}$MnO$_{3}$ $without$ the presence of the 4$f$ magnetic moments of the rare earth ions, and have found two ferroelectric phases with polarization along the $a$ and $c$ axes in a zero magnetic field. A magnetic field induced switching from one to the other ferroelectric phase took plase in which the direction of ferroelectric polarization changed from the a axis to the c axis by the application of magnetic fields parallel to the a axis. In contrast to the case of TbMnO$_{3}$, in which the 4$f$ moments of Tb$^{3+}$ ions play an important role in such a ferroelectric phase switching, the magnetic-field-induced switching between ferroelectric phases in Eu$_{0.595}$Y$_{0.405}$MnO$_{3}$ does not originate from the magnetic transition of the rare-earth 4$f$ moments, but from that of the Mn 3$d$ spins.