  We study the cosmological evolution of BL Lac objects by applying the Ve/Va
analysis to a new sample of 55 objects presented for the first time in this
paper. This sample has been selected from the 239 sources with the brightest
X-ray flux (>4X10^-13 erg s^-1 cm^-2) and relatively bright optical counterpart
(B<20.5) among the ~1600 objects included in the REX survey. The uniform
distribution of the Ve/Va values found in the sample suggests that BL Lac
objects are not affected by a strong cosmological evolution in contrast with
the behavior observed in the emission line AGNs. The Ve/Va analysis applied to
the subsample of the High energy peaked BL Lacs (HBL) does not reveal a
significant departure from a uniform distribution. This result suggests either
that the cosmological evolution is less extreme than that previously found in
other samples or that it is carried out only by a minority of objects, namely
by the most extreme HBLs.
