As measures of concentration, especially for market (industry) concentration based on market shares, a variety of different measures or indices have been proposed. However, the various indices, including the two most widely used ones, the concentration ratio and the Herfindahl-Hirschman index (HHI), lack an important property: the value-validity property. An alternative index with this and other desirable properties is introduced. The new index makes it permissible to properly assess the extent of the concentration and make order and difference comparisons between index values as being true representations of the real concentration characteristic (attribute). Computer simulation data and real market-share data are used in the analysis. It is shown that the new index has a close functional relationship with the HHI index and has a firm theoretical relationship with market power as measured by the price-cost margin. Corresponding modifications to existing merger guidelines are presented.