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A procedure is developed for measuring the complex dielectric permittivity of a material over a broad range of frequencies using a monopole antenna. No restrictions are placed on the electrical size of the antenna. The antenna is calibrated one time by measuring the input admittance in a standard medium with known permittivity, such as air. Next, the admittance is measured with the antenna immersed in a material with unknown permittivity. These two sets of admittances are then used to determine the permittivity of the material. As an application of the procedure, the complex permittivity of the alcohol 1-butanol and saline solutions were measured using a cylindrical monopole antenna. The measured permittivities are in good agreement with those determined by previous investigators.