The hypothetical scanning (HS) method is a general approach for calculating the absolute entropy and free energy by analyzing Boltzmann samples obtained by Monte Carlo (MC) or molecular dynamics techniques. With HS applied to a fluid, each configuration i of the sample is reconstructed by adding its atoms gradually to the initially empty volume, i.e., by placing them in their positions at i using transition probabilities (TPs). At each step of the process, the volume is divided into two parts, the already visited part (the "past") and the "future" part, where obtaining the TP requires calculating partition functions over the future part in the presence of the frozen past. In recent publications, the TPs were calculated approximately by taking into account only partial future. Here we present a "complete HSMC" procedure, where the TPs are calculated from MC simulations carried out over the complete future. The complete HSMC method is applied to systems of liquid argon and the TIP3P model of water, and very good results for the free energy are obtained, as compared with results obtained by thermodynamic integration.