The paper develops a new theory of group discrimination in which the discrimination in favour or against certain groups is simply a coordination device. It is built on the axiom that a person who gets to perform many tasks is more effective in carrying out each task, which implies increasing returns to productivity in doing the same task or strategic complementarity between doing different tasks. The theory helps us understand discrimination in free markets and the finding of some empirical studies that show that people discriminate in job markets against certain groups even when all other traits are held constant. The model gives insight into the relation between group size, discrimination and productivity.