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We show that a quantum system possessing an exact antilinear symmetry, inparticular PT-symmetry, is equivalent to a quantum system having a HermitianHamiltonian. We construct the unitary operator relating an arbitrarynon-Hermitian Hamiltonian with exact PT-symmetry to a Hermitian Hamiltonian. Weapply our general results to PT-symmetry in finite-dimensions and give theexplicit form of the above-mentioned unitary operator and Hermitian Hamiltonianin two dimensions. Our findings lead to the conjecture that non-HermitianCPT-symmetric field theories are equivalent to certain nonlocal Hermitian fieldtheories.Comment: Few typos have been corrected and a reference update

ExactPT-symmetry is equivalent to Hermiticity