A method for producing a clear, vivid and water-fast printed image on a substrate. An ink is used which contains a sublimable dye diffusion thermal transfer coloring agent. The substrate includes a backing layer and an ink absorbent layer on the backing layer. The backing layer is designed to receive the coloring agent therein after sublimation of the coloring agent. The ink is initially delivered to the ink-absorbent layer. The substrate is then heated to cause sublimation of the coloring agent and diffusion of the sublimed coloring agent into the backing layer. Pressure may also be applied during the heating process. In addition, the ink can be retained within an ink cartridge in a printer unit, with the cartridge having at least one ink ejector. Heating of the substrate may then be accomplished by a heating member in the printer unit which contacts the substrate.