The Atkinson index of income inequality is based on a comparison of the average income with the equivalent income, where the equivalent income is defined as the level of income that, if given to everyone, would generate the same social welfare as the existing distribution of income. This paper explores the possibility of extending this approach to the measurement of socioeconomic inequality of health. It assumes a social evaluation function that depends upon two variables: socioeconomic status as well as health status. With a general form of this function, an Atkinson measure is derived, which gives exactly the same result when applied to the socioeconomic variable and when applied to the health variable. The paper examines the properties of the index and suggests various extensions. Copyright © 2012 John Wiley & Sons, Ltd.