In this paper we provide a new methodology to measure opportunity inequality and to decompose overall inequality in an "ethically offensive" and an "ethically acceptable" part. Moreover, we provide some empirical applications of these new evaluation tools: in the first exercise, we compare the income distributions of South and North of Italy on the basis of a measure of opportunity inequality. Then, we repeat the exercise using the cognitive abilities in a sample of 15-year old students. In both circumstances we find that the less developed regions in the South are characterized by greater incidence of inequality of opportunity.