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Abstract The action of the free theory in six spacetime dimensions is explicitly constructed. The variables of the variational principle are prepotentials adapted to the self-duality conditions on the fields. The (3, 1) supersymmetry variations are given and the invariance of the action is verified. The action is first-order in time derivatives. It is also Poincaré invariant but not manifestly so, just like the Hamiltonian action of more familiar relativistic field theories.