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Present probes do not exclude that the neutron ($n$) oscillation into mirrorneutron ($n'$), a sterile state exactly degenerate in mass with the neutron,can be a very fast process, in fact faster than the neutron decay itself. Thisprocess is sensitive to the magnetic field. Namely, if the mirror magneticfield $\vec{B}'$ exists at the Earth, $n-n'$ oscillation probability can besuppressed or resonantly amplified by the applied magnetic field $\vec{B}$,depending on its strength and on the angle $\beta$ between $\vec{B}$ and$\vec{B}'$. We present the results of ultra-cold neutron storage measurementsaiming to check the anomalies observed in previous experiments which could be asignal for $n-n'$ oscillation in the presence of mirror magnetic field $B'\sim0.1$~G. Analyzing the experimental data on neutron loses, we obtain a new lowerlimit on $n-n'$ oscillation time $\tau_{nn'} > 17$ s (95 % C.L.) for any $B'$between 0.08 and 0.17 G, and $\tau_{nn'}/\sqrt{\cos\beta} > 27 $s (95 % C.L.)for any $B'$ in the interval ($0.06\div0.25$) G.

New experimental limits on neutron - mirror neutron oscillations in the presence of mirror magnetic field