  We present the Brera Multi-scale Wavelet ROSAT HRI source catalogue (BMW-HRI)
derived from all ROSAT HRI pointed observations with exposure time longer than
100 s available in the ROSAT public archives. The data were analyzed
automatically using a wavelet detection algorithm suited to the detection and
characterization of both point-like and extended sources. This algorithm is
able to detect and disentangle sources in very crowded fields and/or in
presence of extended or bright sources. Images have been also visually
inspected after the analysis to ensure verification. The final catalogue,
derived from 4,303 observations, consists of 29,089 sources detected with a
detection probability of greater or equal 4.2 sigma. For each source, the
primary catalogue entries provide name, position, count rate, flux and
extension along with the relative errors. In addition, results of
cross-correlations with existing catalogues at different wavelengths (FIRST,
IRAS, 2MASS and GSC2) are also reported. All these information are available on
the web via the DIANA Interface. As an external check, we compared our
catalogue with the previously available ROSHRICAT catalogue (both in its short
and long versions) and we were able to recover, for the short version, \~90% of
the entries. We computed the sky coverage of the entire HRI data set by means
of simulations. The complete BMW-HRI catalogue provides a sky coverage of 732
square degrees down to a limiting flux of ~1E-12 erg/s/cm2 and of 10 square
degrees down to ~1E-14 erg/s/cm2. We were able to compute the cosmological
log(N)-log(S) distribution down to a flux of about 1.2x1E-14 erg/s/cm2.
