The relative permittivity (epsilon(r)) of dimethyl ether (DME) was measured as a function of temperature and pressure in the gaseous, liquid, and supercritical states. The temperature and pressure ranges studied were (303 to 403) K and (0.04 to 33.2) MPa, respectively. The relative permittivity was fitted to the reduced density (rho(r)) using the function (epsilon(r) - 1)/(2 epsilon(r) + 1), and the apparent dipole moment (mu(*)) of the liquid phase was calculated using Kirkwood's theory of molecular polarizability.