A modified form of Carathéodory's Axiom II is proposed. Like Axiom I it is phrased in terms of the work in adiabatic processes and, together with Axiom I, it leads directly to the existence of reversible adiabatic surfaces and hence to the concepts of entropy and absolute temperature. The original Axiom II is shown to be a consequence of the proposed axiom. The multiplicity of possibilities that is characteristic of conclusions based on the original Axiom II is eliminated.