ABSTRACT An in-depth analysis is presented of the accuracy of position of the linear secular resonance g − g5 in the phase space of proper elements, as determined by the recently introduced polynomial fit method. Different attempts to pinpoint the exact location of this resonance are described, leading to improvement in the accuracy of resonance position achieved via local adjustments of the new method and measured in comparison with the corresponding positions of selected asteroids. The resonant state and proper frequencies of the longitude of perihelion of these asteroids are determined, and compared to the catalogue values computed in the course of determination of their synthetic proper elements. The problem of cycle slips, affecting the computation of frequencies, is thoroughly examined and successfully explained, and the procedure of double filtering of the time series of proper values to remove the cycle slips proposed. The results of tests of the new approach have shown that the accuracy of newly determined frequencies is significantly improved with respect to the previously available values.