The Theil index is one of the most popular indices of economic inequality, one reason for which is no doubt due to its convenient additive decomposition property. One of its weaknesses, however, is its lack of any intuitively meaningful interpretations. Another, and more serious, limitation of Theil’s index, as argued in this paper, is its lack of the value-validity property. That is, this index does not meet a particular condition based on metric distances between income-share distributions required in order for the range of potential index values to provide true, realistic, and valid representations of the economic inequality characteristic. After outlining the value-validity condition, this paper derives a simple transformation of Theil’s index that meets this condition to a high degree of approximation. Randomly generated income-share distributions are used to demonstrate and verify the validity of the corrected index. The new index formulation, which is simply a power function of Theil’s index, can then be used to make appropriate and reliable representations of absolute and relative difference comparisons of economic inequalities.