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This paper introduces a new axiom—the unit consistency axiom—into inequality measurement. This new axiom requires the ordinal inequality rankings (rather than the cardinal indices) to be unaffected when incomes are expressed in different units. I argue that unit consistency is an indispensable axiom for the measurement of income inequality. When unit consistency is combined with decomposability, I show that the unit-consistent decomposable class of inequality measures is a two-parameter extension of the one-parameter generalized entropy class. The extended class accommodates a variety of value judgments and includes different types of inequality measures.