Technical Abstract: The assemblage of a core collection from very large germplasm collections is problematic. The computing resources needed to carry out genetic distance calculations and comparisons with commonly-available programs is prohibitively large. We have developed a method which assembles a core collection by maximizing the selected diversity (measured as mean Euclidian distance) from within groups of accessions defined by species, subspecies, and geographic origin. The effectiveness of the method was tested on a collection of 17,798 annual Medicago accessions that had been evaluated for 24 characters. The method resulted in a core collection of 1705 accessions that represented 90% of the extremes of the 24 characters, indicating that the entire range of the characters was represented in most cases. Accessions representing the extremes missed easily could be added to the core collection. The method used requires relatively small computing resources and should be useful to curators of large germplasm collections.