We propose the "Flux-mediated epitaxy" as a novel concept for the growth of single crystalline films of incongruent, volatile, and high-temperature-melting compounds. In flux-mediated eptitaxy, by supplying materials precursors from the gas phase through the liquid flux films pre-deposited on the substrate, a quasi-thermodynamic equilibrium condition is obtained at the interface between the growing films and the flux films. This process has been demonstrated in this paper by fabricating ferroelectric Bi 4 Ti 3 O 12 films, which has volatile Bi oxide.The most important step in this process is the selection of the right flux material, which is hard to predict due to the lack of an appropriate phase diagram. In order to overcome this problem, we have selected the combinatorial approach. A series of ternary flux libraries composed of two self-fluxes (