Ink-jetting printing apparatus and printing method

When printing using a dye ink and a pigment ink, and in addition, one of these treatment liquid inks insoluble, two inks made of pigment ink and dye ink composition. After the pigment ink onto the printing medium, the dye ink is applied to cover the pigment ink. After mixing these inks on the printing medium, then applying the processing liquid ink insoluble. Alternatively, it is possible to use the mixed ink, the ink mixing does not require a dispersant composed of a pigment ink and dye ink. After application of this mixed ink onto the printing medium, the treatment liquid is applied to make the ink insoluble. Thus, the pigment ink can be solved by the mixed ink and the dye ink with the treatment liquid caused by the reaction or "crack", "soaking out", "overflow" or reduce the OD value and so on, thereby obtaining a high quality printing.