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Spurious contributions from electrode polarization (EP) are a major nuisance in dielectric measurements of biological tissues and hamper accurate determination of tissue properties in the audio/radiofrequencies. Various electrode geometries and/or treatments have been employed traditionally to reduce EP contributions, although none succeeded to completely remove EP from measurements on tissues for all practical frequency ranges. A method of correction for contributions of EP to the dielectric properties of tissues is proposed. The method is based on modeling the electrode impedance with suitable functions and on the observation that certain parameters are only dependent on electrodes properties and can thus be determined separately. The method is tested on various samples with known properties, and its usefulness is demonstrated with samples of normal and cancerous human female breast tissue. It is observed that the dielectric properties of the tissues over the frequency range 40 Hz-100 MHz are significantly different among different types of breast tissue. This observation is used further to demonstrate that, by scanning the tip of the measuring dielectric probe (with modest spatial resolution) across a sample of excised breast tissue, significant variations in the electrical properties are detected at a position where a tumor is located. This study shows that dielectric spectroscopy has the potential to offer a viable alternative to the current methods for detection of breast cancer in vivo.