A new high precision measurement of the J/ψ- and ψ′-meson masses has been performed at the VEPP-4M collider using the KEDR detector. The resonant depolarization method has been employed for the absolute calibration of the beam energy. The following mass values have been obtained: Formula Not Shown The relative measurement accuracy has reached 4×10−6 for J/ψ and 7×10−6 for ψ′, approximately 3 times better than in the previous precise experiments.