In order to improve efficacy of screening mammography, in recent years, we have been investigating the feasibility of applying a resonance-frequency based electrical impedance spectroscopy (REIS) technology to noninvasively detect breast abnormalities that may lead to the development of cancer in the near-term. Despite promising study-results, we found that REIS suffered from relatively poor reproducibility due to perturbations in electrode placement, contact pressure variation on the breast, as well as variation of the resonating inductor. To overcome this limitation, in this study, we propose and analyze a new paradigm of Dielectric Relaxation Spectroscopy (DRS) that measures polarization-lag of dielectric signals in breast-capacitance when excited by the pulses or sine waves. Unlike conventional DRS that operates using the signals at very high frequencies (GHz) to examine changes in polarization, our new method detects and characterizes the dielectric properties of tissue at low frequencies (≤10 MHz) due to the advent of inexpensive oscillators that are accurate to 1 pico-second (used in GPS receivers) as well as measurement of amplitudes of 1 ppm or better. From theoretical analysis, we have proved that the sensitivity of new DRS in detecting permittivity of water increased by ≥80 times as compared to conventional DRS, which operates at frequencies around 4GHz. By analyzing and comparing the relationship between the new DRS and REIS, we found that this DRS has potential advantages in enhancing repeatability from various readings, including temperature-insensitive detection, and yielding higher resolution or sensitivity (up to 100 Femtofarads).