Ions in the plasmasphere show various spectral structures on their energy spectrograms. In this study we investigate an energy-dispersed narrow band structure on the energy-time spectrogram using the observations from the Helium Oxygen Proton Electron (HOPE) instrument onboard the Van Allen Probes (VAP) satellites. The band structure shows that the energy of the peak flux gradually decreases as the satellite moves away from Earth while keeping the width of the flux in energy narrow. In most cases, the nose-like structures, which have much broader energy bands, are observed in the preceding orbit. The band structure appears on the lowest energy edge of the preceding nose-like structure after the nose-like structure vanishes. Statistical analysis for the observations from October 2012 to December 2017 shows that the band structure occurs more frequently in the dusk sector and the energy of its innermost tip depends on the magnetic local time similar to the nose-like structure. These results suggest that loss of ions in the nose-like structure leads to the formation of the band structure. However, not all nose-like structures come to the band structure. Most of the band structures are observed for a period when solar wind speed is slow while the nose-like structures disappear without the formation of the band structure when they are formed under fast solar wind conditions.