The mechanism of the double-proton transfer in the formamide-formamidine dimer, which is the simplest model resembling the hydrogen bonding pattern in the adenine-thymine base pair, has been studied by means of ab initio post-Hartree-Fock calculations. The optimizations of all local minima and transition states were performed for both the gas phase and water solution using density functional theory (B3LYP), second-order Moller-Plesset theory, and the quadratic configuration interaction method using various basis sets. Additional optimizations of the structures with explicitly included water molecules were performed at the B3LYP level of theory. The two-dimensional adiabatic surfaces have been calculated for the process of double-proton transfer in both the gas phase and a polar surrounding. The results of the calculations indicate that the gas-phase double-proton transfer possesses a concerted and asynchronous mechanism. However, due to the stabilization of the zwitterionic structure by a polar medium, the latter becomes a local minimum in the water solution where the reaction proceeds through a stepwise mechanism.