  A new version of the event generator BABAYAGA is presented, which is based on
an original matching of the Parton Shower approach with the complete exact
O(alpha) matrix element for the inclusion of the QED radiative corrections to
the Bhabha process at flavour factories. The theoretical accuracy of the
improved generator is conservatively estimated to be 0.2%, by comparison with
independent calculations. The generator is a useful tool for precise luminosity
determination at flavour factories, for center of mass energies below 10 GeV.
