In recent years attention has been drawn to several shortcomings of the Concentration Index, a frequently used indicator of the socioeconomic inequality of health. Some modifications have been suggested, but these are only partial remedies. This paper proposes a corrected version of the Concentration Index which is superior to the original Concentration Index and its variants, in the sense that it is a rank-dependent indicator which satisfies four key requirements (transfer, level independence, cardinal invariance, and mirror). The paper also shows how the corrected Concentration Index can be decomposed and generalized.