Several applications of Electrical Bioimpedance (EBI) make use of Cole parameters as base of their analysis, therefore Cole parameters estimation has become a very common practice within Multifrequency- and EBI spectroscopy. EBI measurements are very often contaminated with the influence of parasitic capacitances, which contributes to cause a hook-alike measurement artifact at high frequencies in the EBI obtained data. Such measurement artifacts might cause wrong estimations of the Cole parameters, contaminating the whole analysis process and leading to wrong conclusions. In this work, a new approach to estimate the Cole parameters from the real part of the admittance, i.e. the conductance, is presented and its performance is compared with the results produced with the traditional fitting of complex impedance to a depressed semi-circle. The obtained results prove that is feasible to obtain the full Cole equation from only the conductance data and also that the estimation process is safe from the influence capacitive leakage.