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 _ { H } < 1.3 \times 10 ^ { 20 } cm ^ { -2 } ) .
In total , 7 sources out of 27 are heavily obscured in the X-ray ( N _ { H } > 10 ^ { 22 } cm ^ { -2 } ) , corresponding to a surface density of 0.7 deg ^ { -2 } at the flux limit the sample ( 4-7 \times 10 ^ { -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 _ { [ 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 ( \sim 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 .