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)

9 pages, 9 figures, submitted to A&A, version with high quality figures available at http://www.aai.ee/~maret/2dfgr.html