  We present a carefully selected sub-sample of Swift Long Gamma-ray Bursts
(GRBs), that is complete in redshift. The sample is constructed by considering
only bursts with favorable observing conditions for ground-based follow-up
searches, that are bright in the 15-150 keV Swift/BAT band, i.e. with 1-s peak
photon fluxes in excess to 2.6 ph s^-1 cm^-2. The sample is composed by 58
bursts, 52 of them with redshift for a completeness level of 90%, while another
two have a redshift constraint, reaching a completeness level of 95%. For only
three bursts we have no constraint on the redshift. The high level of redshift
completeness allows us for the first time to constrain the GRB luminosity
function and its evolution with cosmic times in a unbiased way. We find that
strong evolution in luminosity (d_l=2.3\pm 0.6) or in density (d_d=1.7\pm 0.5)
is required in order to account for the observations. The derived redshift
distribution in the two scenarios are consistent with each other, in spite of
their different intrinsic redshift distribution. This calls for other
indicators to distinguish among different evolution models. Complete samples
are at the base of any population studies. In future works we will use this
unique sample of Swift bright GRBs to study the properties of the population of
long GRBs.
