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The dielectric constant of Co4Nb2O9 shows an obvious upturn below Néel temperature (TN), and the magnetic field enhances this anomaly. Thus the magnetodielectric effect exists in the entire temperature region below TN, not only near TN as reported previously. At the same time, the strain exhibits a drop below TN, and the magnetic field suppresses this anomaly, demonstrating magnetoelastic coupling in Co4Nb2O9. The origin of dielectric anomaly and magnetodielectric effect below TN may be related to the phonon mode shifts induced by magnetoelastic coupling.