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This paper describes a new method of measuring the complex relative permittivity ε* of low-loss liquids and granulated materials up to the L-band in the microwave range, based on the six-port technique. The novel feature of this method is the determination of ε* directly from the intersection of three circles in the complex ε*-plane. Furthermore, neither liquids nor granulated materials are used as calibration standards; instead, a matched load and nine adjustable short circuits are employed as standards. The ambiguity usually found in several reported methods is completely eliminated by the already consolidated six-port technique. Results of computer simulations are presented and discussed.