Ground-based observations have shown that Jupiter is a two-component source of microwave radio emission: thermal atmospheric emission and synchrotron emission from energetic electrons spiralling in Jupiter's magnetic field. Later in situ measurements confirmed the existence of Jupiter's high-energy electron-radiation belts, with evidence for electrons at energies up to 20[?]MeV. Although most radiation belt models predict electrons at higher energies, adiabatic diffusion theory can account only for energies up to around 20[?]MeV. Unambiguous evidence for more energetic electrons is lacking. Here we report observations of 13.8[?]GHz synchrotron emission that confirm the presence of electrons with energies up to 50[?]MeV; the data were collected during the Cassini fly-by of Jupiter. These energetic electrons may be repeatedly accelerated through an interaction with plasma waves, which can transfer energy into the electrons. Preliminary comparison of our data with model results suggests that electrons with energies of less than 20[?]MeV are more numerous than previously believed.