We analyze the power spectra measured by the radio receiver of the Unified Radio and Plasma Wave experiment on Ulysses during its passage through the Jovian inner magnetosphere from ~9 RJ in the outskirts of the Io plasma torus to ~13 RJ near the plasma sheet. Below the plasma frequency fp, these spectra are weakly banded between gyroharmonics. These observations were interpreted by Meyer-Vernet et al. [1993> as quasi-thermal fluctuations in Bernstein waves. We show that above fp each observed gyroharmonic band falls off very abruptly on its high-frequency side. We interpret it as the forbidden band predicted by the Bernstein wave dispersion equation between the so-called fQ frequency and the consecutive gyroharmonic, that is, a region where no Bernstein wave can propagate. This allows a determination of the local cold plasma frequency and thus of the core electron density with a ~16% uncertainty. As a consistency check, we show that the fQ thus determined are very close to the frequencies of the resonances excited by the relaxation sounder on Ulysses.¿ 1997 American Geophysical Union