Mirror matter is considered as a candidate for dark matter. In connection with this an experimental search for neutron - mirror neutron (nn) transitions has been carried out using storage of ultracold neutrons in a trap with different magnetic fields. As a result, a new limit for the neutron - mirror neutron oscillation time has been obtained, tau_osc >= 448 s (90% C.L.), assuming that there is no mirror magnetic field larger than 100 nT. Besides a first attempt to obtain some restriction for mirror magnetic field has been done.
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