  We present the results of a deep (1.1 Ms) observation of the Coma cluster of
galaxies in the 18-30 keV band with the IBIS/ISGRI imager on board the INTEGRAL
satellite. We show that the source extension in the North-East to South-West
(SW) direction ($\sim 17'$) significantly exceeds the size of the point spread
function of ISGRI, and that the centroid of the image of the source in the
18-30 keV band is displaced in the SW direction compared to the centroid in the
1-10 keV band. To test the nature of the SW extension we fit the data assuming
different models of source morphology. The best fit is achieved with a diffuse
source of elliptical shape, although an acceptable fit can be achieved assuming
an additional point source SW of the cluster core. In the case of an elliptical
source, the direction of extension of the source coincides with the direction
toward the subcluster falling onto the Coma cluster. If the SW excess is due to
the presence of a point source with a hard spectrum, we show that there is no
obvious X-ray counterpart for this additional source, and that the closest
X-ray source is the quasar EXO 1256+281, which is located $6.1'$ from the
centroid of the excess. Finally, we show that the hard X-ray emission coincides
with the 1.4 GHz radio emission, which suggests that the hard X-ray emission
comes from the same population of electrons that is responsible for radio
haloes through synchrotron emission.
