We present results of the analysis of an unusually long narrow-band emission in the Pc1 range with increasing carrier frequency. The event was observed against the background of the main phase of a strong magnetic storm caused by arrival of a high-speed solar wind stream with a shock wave in the stream head and a long interval of negative vertical component of the interplanetary magnetic field. Emission of approximately 9-hour duration had a local character, appearing only at three stations located in the range of geographical longitude λ=100–130 E and magnetic shells L=2.2–3.4. The signal carrier frequency grew in a stepped mode from 0.5 to 3.5 Hz. We propose an emission interpretation based on the standard model of the generation of ion cyclotron waves in the magnetosphere due to the resonant wave-particle interaction with ion fluxes of moderate energies. We suppose that a continuous shift of the generation region, located in the outer area of the plasmasphere, to smaller L-shell is able to explain both the phenomenon locality and the range of the frequency increase. A narrow emission frequency band is associated with the formation of nose-like structures in the energy spectrum of the ion fluxes penetrating from the geomagnetic tail into magnetosphere. We offer a possible speculative scenario of the processes leading to the generation of the observed emission. The scenario contains specific values of the generation region position, plasma density, magnetic field, and resonant proton energies. We discuss morphological differences of the emissions considered from known types of geomagnetic pulsations, and reasons for the occurrence of this unusual event.