In this report, we modify the model of Arridge et al. (2011) which was proposed to describe the shape of the magnetodisk of Saturn and its north-south oscillations near the planetary rotation period. The modification is based on the recent results of Provan et al. (2011, 2012) and Andrews et al. (2012), who have shown that the magnetic modulations near the current sheet exhibit dual periodicities, and derived magnetic phase functions for the northern and southern period modulations from the magnetic field data. Using a modified model in which the effects of both modulations are included, specifically related to the modulations of the radial component of the magnetic field, we show that the oscillations can be modeled without the use of an arbitrarily assigned oscillation phase value as employed in the previous work of Szego et al. (2012). In addition, the best fit amplitudes of the two oscillations are found to be nearly constant for a majority of the magnetodisk data analyzed, such that a single model with one fixed parameter fits well to the data for a majority of the passes. ; Work at Leicester was supported by STFC grant ST/H002480/1. ; Peer-reviewed ; Publisher Version