The LINER nucleus of the nearby spiral galaxy M81 was pointed by BeppoSAX, which caught it at the highest (2-10) keV flux level observed so far. The LECS, MECS and PDS data, extending over (0.1-100) keV, are used to investigate the physical similarities and differences between LINERs and AGNs. The continuum is well fitted by a power law of photon index sim 1.84, modified by little absorption due to cold material. Superimposed on the continuum BeppoSAX detects a 6.7 keV emission line (confirming an ASCA result) and an absorption edge at 8.6 keV. Both spectral features are consistent with being produced by iron at the same high ionization level, and probably also with the same column density. So, we suggest that they originate from transmission through highly ionized thin material. Concerning the origin of the continuum emission, we do not observe signs of reflection from the optically thick material of an accretion disk, as usually found in Seyfert 1s (a 6.4 keV emission line and a broad bump peaking at 10-20 keV). The low bolometric luminosity of the nucleus of M81 is consistent with being produced by advection dominated accretion; in this case the X-ray emission should be dominated by Comptonization, rather than by bremsstrahlung, in order to reproduce the steep spectrum observed over the (0.1-100) keV band.