We introduce a general decomposition method applicable to all forms of bivariate rank dependent indices of socioeconomic inequality in health, including the concentration index. The technique is based on recentered influence function regression and requires only the application of OLS to a transformed variable with similar interpretation. Our method requires few identifying assumptions to yield valid estimates in most common empirical applications, unlike current methods favoured in the literature. Using the Swedish Twin Registry and a within twin pair fixed effects identification strategy, our new method finds no evidence of a causal effect of education on income-related health inequality.