A new method for the study of the star formation histories of nearby galaxies with resolved stars is presented here. Rather than adopting traditional methods of creating synthetic color-magnitude diagrams (CMDs) with various star formation histories, the approach taken is to create a set of CMDs which can be combined linearly to reproduce almost any star formation history, and use a numerical fit to solve the problem. In addition, a quantitative fit parameter for determining the similarity of an observed and a theoretical CMD is presented, along with a number of tests of this parameter. Finally, a rigorous test of the method is given. (C) 1997 Elsevier Science B.V.