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A novel measurement technique of strong-phase differences between the decay amplitudes of D0 and D0 mesons is introduced which exploits quantum-correlated DD pairs produced by e+e−collisions at energies above the ψ(3770) production threshold, where DD pairs are produced in both even and odd eigenstates of the charge-conjugation symmetry. Employing this technique, the first determination of a D0–D0 relative strong phase is reported with such data samples. The strong-phase difference between D0 → K−π+ and D0 → K−π+ decays, δDK π, is measured to be δDK π = (192.8+11.0+1.9-12.4-2.4)°, using a dataset corresponding to an integrated luminosity of 7.13 fb−1 collected at center-of-mass energies between 4.13–4.23 GeV by the BESIII experiment.