An index of Inequality is constructed which decomposes into two components, corresponding to vertical and "horizontal" equity respectively. Horizontal equity Is defined in terms of changes in the ordering of a distribution. The proposed index is a function to two inequality aversion parameters. One empirical application is for comparison of a pre-tax distribution with a post-tax distribution, and an example of this is given for the distribution of incomes in the UK in 1977. There is a trade-off between "horizontal"and vertical equity, and for particular combinations of the inequality aversion parameters the original distribution will be preferred to the final distribution. The paper concludes with an application of the proposed index to a model of optimal taxation.