  Hydrocarbon species, and in particular CH$_4$, play a key role in the
stratosphere--thermosphere boundary of Jupiter, which occurs around the
$\mu$-bar pressure level. Previous analyses of solar occultation, He and
Ly-$\alpha$ airglow, and ISO/SWS measurements of the radiance around 3.3 $\mu$m
have inferred significantly different methane concentrations. Here we aim to
accurately model the CH$_4$ radiance at 3.3 $\mu$m measured by ISO/SWS by using
a comprehensive non-local thermodynamic equilibrium model and the most recent
collisional rates measured in the laboratory for CH$_4$ to shed new light onto
the methane concentration in the upper atmosphere of Jupiter. These emission
bands have been shown to present a peak contribution precisely at the $\mu$-bar
level, hence directly probing the region of interest. We find that a high
CH$_4$ concentration is necessary to explain the data, in contrast with the
most recent analyses, and that the observations favour the lower limit of the
latest laboratory measurements of the CH$_4$ collisional relaxation rates. Our
results provide precise constraints on the composition and dynamics of the
lower atmosphere of Jupiter.
