In this paper we propose to measure inequality of educational achievements by constructing a Gini index on educational attainments. We then use the proposed measure to analyse the relationship between inequality in incomes and educational achievements (in terms of both the average attainments and its concentration). Even if theoretical considerations suggest a non-linear relationship between these two measures of inequality, actual data indicate that average years of education have a stronger negative impact on measured income inequality. Multivariate regressions also prove that, once we take into account the negative correlation between average educational achievement and its dispersion, the relationship between income inequality and average years of schooling is U-shaped, with a lower turning point at 6.5 years. Income inequality is also negatively related to per capita income and positively related to capital/output ratio and government expenditure in education.