This paper shows that when the health sector variable whose inequality is being investigated is binary, the minimum and maximum possible values of the concentration index (CI) are equal to the mean minus one and one minus the mean, respectively. Thus as the mean increases, the range of the possible values of the CI shrinks, tending to zero as the mean tends to one and the CI tends to zero. This can be handled by normalizing the CI to reflect the minimum and maximum feasible values. Examples are presented, for a variety of indicators and countries, showing the consequences of not applying the normalization.