Hard X-ray radiation has been detected for the first time in the Coma cluster by BeppoSAX. Thanks to the unprecedented sensitivity of the Phoswich Detection System (PDS) instrument, the source has been detected up to ~80 keV. There is clear evidence (4.5 sigma) for non-thermal emission in excess of thermal above ~25 keV. The hard excess is very unlikely due to X Comae, the Seyfert 1 galaxy present in the field of view of the PDS. A hard spectral tail due to inverse Compton on CMB photons is predicted in clusters, like Coma, with radio halos. Combining the present results with radio observations, a volume-averaged intracluster magnetic field of ~0.15 micro G is derived, while the electron energy density of the emitting electrons is ~7x10**-14 erg/cm**3.
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