  We introduce GalWeight, a new technique for assigning galaxy cluster
membership. This technique is specifically designed to simultaneously maximize
the number of bona fide cluster members while minimizing the number of
contaminating interlopers. The GalWeight technique can be applied to both
massive galaxy clusters and poor galaxy groups. Moreover, it is effective in
identifying members in both the virial and infall regions with high efficiency.
We apply the GalWeight technique to MDPL2 \& Bolshoi N-body simulations, and
find that it is $> 98\%$ accurate in correctly assigning cluster membership. We
show that GalWeight compares very favorably against four well-known existing
cluster membership techniques (shifting gapper, den Hartog, caustic, SIM). We
also apply the GalWeight technique to a sample of twelve Abell clusters
(including the Coma cluster) using observations from the Sloan Digital Sky
Survey. We end by discussing GalWeight's potential for other astrophysical
applications.
