We recently introduced an iterative method to compute quantum time correlation functions [Bonella et al. J. Chem.Phys 133 (16) 164105 (2010)]. There, the thermal part of the correlation function is treated exactly and, similar to the linearization techniques, at zero order of iteration only classical dynamics is required. In this work, we propose a new scheme for the zero order iteration of the method which significantly improves the efficiency of the calculations for high dimensional model systems.