Correlations of ambient seismic noise are now widely used to retrieve the Earth response between two points. In this study, we reconstruct the surface-wave Green's function by iterating the correlation process over the tail of the noise-based correlation function. It has been demonstrated that the so-called C 3 function shows the surface-wave part of the Green's function. Using data from 150 continuously recording stations in Europe, the C 3 results help in the extraction of the travel-times from noise-based measurements, especially through the suppression of effects caused by non-isotropic source distributions. We present the results of the next iterative step (i.e. C 5), which show that some coherent signal is still present in the coda of the C 3 function, and we investigate the evolution of the reconstruction of the Green's function throughout the iteration process. Finally, we discuss the interest of combining information from the different correlation functions to improve noise-based tomography analysis.