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We present the Palermo Swift-BAT hard X-ray catalogue obtained from the analysis of the the data relative to the first 39 months of the Swift mission. We have developed a dedicated software to perform data reduction, mosaicking and source detection on the BAT survey data. We analyzed the BAT dataset in three energy bands (14-150 keV, 14-30 keV, 14-70 keV), obtaining a list of 962 detections above a significance threshold of 4.8 standard deviations. The identification of the source counterparts was pursued using three strategies: cross-correlation with published hard X-ray catalogues, analysis of field observations of soft X-ray instruments, cross-correlation with the SIMBAD databases. The survey covers 90% of the sky down to a flux limit of 2.5x10E-11 erg/cm2/s and 50% of the sky down to a flux limit of 1.8x10E-11 erg/cm2/s in the 14-150 keV band. We derived a catalogue of 754 identified sources, of which ~69% are extragalactic, ~27% are Galactic objects, ~4% are already known X-ray or gamma ray emitters whose nature has not been determined yet. The integrated flux of the extragalactic sample is ~1% of the Cosmic X-ray background in the 14-150 keV range.