We present a new sampling and analysis scheme for calculating the potential of mean force (PMF) of systems studied by steered molecular dynamics simulations. This scheme, which we call the bin-passing method, is based on the forwardreverse (FR) method (due to I. Kosztin and co-workers, Kosztin et al. J. Chem. Phys. 2006, 124(6), 064106) and arguments based on the second law of thermodynamics. Applying the bin-passing method results in enhanced sampling, better separation of the reversible and irreversible work distributions, and faster convergence to the underlying PMF of the system under study. Post-simulation analysis is performed using a purpose-built software that we have made publicly available at https://github.com/1particle/bin-passing_analyzer under the terms of the GNU General Public License (version 3). Three examples are provided, for systems of varying sizes and complexities, to demonstrate the efficiency of this method and the quality of the results: for the dissociation PMF of NaCl in water, the bin-passing method obtains PMFs in excellent agreement with that obtained for the same system and using the same force-field through static (equilibrium) methods. The bin-passing method gives a very symmetric PMF for passage of a single water molecule through a DPPC bilayer, and the resultant PMF leads to permeability values in better agreement with experiments than those obtained through previous simulation studies. Finally, we consider the interaction of the antimicrobial peptide HHC-36 with two model membranes and employ the bin-passing method to obtain the PMFs for peptide adsorption to the membranes. The characteristics of these PMFs are consistent with the qualities established for the HHC-36 peptide through in vivo and in vitro experiments, as a non-toxic strong antimicrobial agent.