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We consider general theories of a massive spin-2 particle $h_{\mu\nu}$ on aMinkowski background. A decomposition of $h_{\mu\nu}$ in terms of helicityeigenstates allows us to directly test whether any given theory possesses aconsistent description as a massive spin-2 representation of the Poincar\'egroup. We demonstrate (i) that any nonlinear theory with an Einsteinianderivative structure either contains ghosts or does not describe a weaklycoupled spin-2 and (ii) that there exists a two-parameter family ofnon-Einsteinian cubic self-interactions which constitute a ghost-free massivespin-2 theory.

On ghosts in theories of self-interacting massive spin-2 particles