Adaptive Umbrella Sampling: Self-consistent Determination of the Non-Boltzmann Bias Abstract: A self-consistent procedure is described for the determination of the non-Boltzmann bias for the Umbrella Sampling technique of Valleau, Patey and Torrie. The new procedure offers more reliable results with less human interference. The problem of matching several differently normalized probability distributions on overlapping domains has been treated in detail. The algorithm has been tested on the calculation of the solvent contribution to the free energy difference between the C₇ and a_R conformation of the alanine dipeptide, treated earlier with the conventional umbrella sampling technique.