The Voyager 2 measurements of energetic (~1 MeV/nucleon) H3 molecules in Jupiter's magnetosphere provided strong evidence that the planet's ionosphere is an important plasma source in the Jovian environment (Hamilton et al., 1980). During the Ulysses spacecraft encounter with Jupiter in February 1992 the Heliosphere Instrument for Spectra, Composition, and Anisotropy at Low Energies (HI-SCALE) on this satellite also detected significant fluxes of energetic H3 molecules. These molecules were measured throughout the dayside inbound pass (near the plasma sheet) as well as during the outbound pass at high Jovian latitudes on the duskside. The spectral shapes of the energetic 4He and the H3 are found to be similar over the range ~0.6--1.6 MeV/nucleon, with a power law spectral slope of n~3. The abundance ratio R (≡H3/4He) is found to be ~0.1 over this energy range for the inbound pass and to vary from ~0.2 at ~0.6 MeV/nucleon to ~0.1 at ~1.6 MeV/nucleon at duskside high latitudes. These observations, especially those from high latitudes, confirm that the energetic molecules must be accelerated out of the Jovian topside ionosphere into the magnetosphere. ¿ American Geophysical Union 1993