  The idea of a hidden sector of mirror partners of elementary particles has
attracted considerable interest as a possible candidate for dark matter.
Recently it was pointed out by Berezhiani and Bento that the present
experimental data cannot exclude the possibility of a rapid oscillation of the
neutron n to a mirror neutron n' with oscillation time much smaller than the
neutron lifetime. A dedicated search for vacuum transitions n->n' has to be
performed at weak magnetic field, where both states are degenerate. We report
the result of our experiment, which compares rates of ultracold neutrons after
storage at a weak magnetic field well below 20 nT and at a magnetic field
strong enough to suppress the seeked transitions. We obtain a new limit for the
oscillation time of n-n' transitions, tau_osc (90% C.L.) > 414 s. The
corresponding limit for the mixing energy of the normal and mirror neutron
states is delta_m (90% C.L.) < 1.5x10-18 eV.
