  We create a new catalogue of groups and clusters for the 2dF GRS final
release sample. We show that the variable linking length friends-of-friends
(FoF) algorithms used so far yield groups with sizes that grow systematically
with distance from the observer, but FoF algorithms with a constant linking
length are free from this fault. We apply the FoF algorithm with a constant
linking length for the 2dF GRS, compare for each group its potential and
kinetic energies and remove galaxies with excess random velocities. Our sample
contains 7657 groups in the Northern part, and 10058 groups in the Southern
part of the 2dF survey with membership Ng >= 2. We analyze selection effects of
the catalogue and compare our catalogue of groups with other recently published
catalogues based on the 2dF GRS. We also estimate the total luminosities of our
groups, correcting for group members fainter than the observational limit of
the survey. The cluster catalogues are available at our web-site
(http://www.aai.ee/~maret/2dfgr.html)
