  Galaxy groups provide the means for a great diversity of studies that
contribute to a better understanding of the structure of the universe on a
large scale and allow the properties of galaxies to be linked to those of the
host halos. However, the identification of galaxy systems is a challenging task
and therefore it is necessary to improve the techniques involved as much as
possible. In view of the large present and forthcoming galaxy catalogues, we
propose, implement, and evaluate an algorithm that combines the two most
popular techniques used to identify galaxy systems. The algorithm can be easily
applied to any spectroscopic galaxy catalogue, but here we demonstrate its use
on the Sloan Digital Sky Survey. Assuming that a galaxy group is a
gravitationally bounded system that has at least one bright galaxy, we begin by
identifying groups with a Friends-Of-Friends algorithm adapted to fit this
definition. In view of the shortcomings of this method, particularly the lack
of ability to identify low-number groups, and consequently the inability to
study the occupation of halos throughout the mass range, we improve it by
adding a halo-based procedure. To assess the performance, we construct a mock
catalogue from a semi-analytical model to compare the groups identified using
our method with those obtained from the simulation. The comparison of groups
extracted using our method with those of a mock catalogue shows that the
proposed algorithm provides excellent results. The modifications introduced to
the Friends-Of-Friends algorithm in the first part of the procedure to fit the
adopted group definition gave reliable groups. Furthermore, the incorporation
of the halo-based method reduces the interlopers while more accurately
reproducing the number of galaxies per group. As a specific application, we use
the algorithm to extract groups from the Sloan Digital Sky Survey.
