In the present study we use all-sky energy-resolved (5-55 keV) energetic neutral atom (ENA) maps obtained by the Ion and Neutral CAmera (INCA) on board Cassini during the time period DOY 265/2003 to 268/2003, to investigate the properties of the peak-to-basin ENA emissions in the direction of the heliotail. Our conclusions can be summarized as follows: (1) a relatively smooth boundary (called "transition region") between the very low (basin) and high (tail) ENA emissions from the heliosheath, with a spatial width of ~30° deg in ecl. longitude, that no theory had predicted to date, is identified in the energy range of 5-55 keV; (2) the ENA intensity gradient in this transition region is almost invariant as a function of both ecl. Latitude and energy, with an average value of ~2.4% per degree; (3) the deduced partial plasma pressure distributions in the 5-55 keV energy range are consistent with the ENA intensity distributions in the same energy range, while the ENA intensity gradient translates to a corresponding partial pressure gradient that occurs in the transition region; and (4) this partial pressure gradient is possibly not consistent with a tail magnetic field configuration that is similar to the measured magnetic fields by the Voyagers in the nose hemisphere.