Prior information about the average dielectric properties of breast tissue can be implemented in microwave breast imaging techniques to improve the results. Rapidly providing this information relies on acquiring a limited number of measurements and processing these measurement with efficient algorithms. Previously, systems were developed to measure the transmission of microwave signals through breast tissue, and simplifications were applied to estimate the average properties. These methods provided reasonable estimates, but they were sensitive to multipath. In this paper, a new technique to analyze the average properties of breast tissues while addressing multipath is presented. Three steps are used to process transmission measurements. First, the effects of multipath were removed. In cases where multipath is present, multiple peaks were observed in the time domain. A Tukey window was used to time-gate a single peak and, therefore, select a single path through the breast. Second, the antenna response was deconvolved from the transmission coefficient to isolate the response from the tissue in the breast interior. The antenna response was determined through simulations. Finally, the complex permittivity was estimated using an iterative approach. This technique was validated using simulated and physical homogeneous breast models and tested with results taken from a recent patient study.