The XMM-

This paper presents the analysis of a statistically complete sample of 28 serendipitous X-ray sources selected in 82 pointed XMM-Newton fields down to a count-rate of 0.002 counts s-1 (4.5–7.5 keV energy band). This is the first sample selected in this energy range to have complete spectroscopic identifications and redshift determinations for all the objects. Apart from one Galactic source (an interacting binary), all the objects are AGNs. Their optical and X-ray properties (derived from the spectral analysis of the XMM-EPIC data) are compared together. The good correlation between the optical spectral type and the X-ray absorption properties supports the AGN unified model. Only one object that does not fit the relation between optical and X-ray absorption is found, namely a Seyfert 1.9 with no evidence of obscuration in the X-ray band ($N_{\rm H}<1.3\times10^{20}$ cm-2). In total, 7 sources out of 27 are heavily obscured in the X-ray ($N_{\rm H}>10^{22}$ cm-2), corresponding to a surface density of 0.7 deg-2 at the flux limit the sample ($4{-}7\times10^{-14}$ erg s-1 cm-2 in the 4.5–7.5 keV energy band). Among these obscured objects, two sources show a large (intrinsic) luminosity ($L_{\rm{[2{-}10~keV]}}>10^{44}$ erg s-1) and are thus classified as type 2 QSO. Finally, we have compared the fraction of X-ray absorbed AGNs (26%) with that predicted by the current XRB synthesis models at the flux limit of the survey. We find that the models significantly (~90% confidence level) over predict the fraction of absorbed AGNs thus confirming also in this hard energy band (4.5–7.5 keV) similar results recently obtained in the 2–10 keV band