The present invention relates to a thermal transfer ink ribbon cassette, a thermal transfer printer and a control method for the same. In particular, the invention relates to a thermal transfer ink ribbon cassette that is easily attached to and removed from a printer, to a printer to which such an ink ribbon cassette is attached and to a method for controlling such a printer. Conventionally, a thermal transfer ink ribbon is used for transferring a thermal transfer ink to a printing surface of a recording medium. When a color image is to be printed with the thermal transfer ink ribbon, three color thermal transfer ink ribbons of yellow, magenta and cyan are used, and each color thermal transfer ink ribbon has its own thermal transfer ink layer. The thermal transfer ink ribbon is made of a polyethylene terephthalate (PET) film or a polyamide film which is colored in yellow, magenta or cyan. Also, such a thermal transfer ink ribbon can be prepared by coloring a conventional resin sheet with pigment or dye. The thermal transfer ink ribbon is contained in a thermal transfer ink ribbon cassette which is a cassette that contains the thermal transfer ink ribbon. In general, a thermal transfer ink ribbon cassette has such a structure that it is removably attached to a printer. Thus, when it is desired to print an image with the thermal transfer ink ribbon contained in the thermal transfer ink ribbon cassette, the thermal transfer ink ribbon cassette is mounted in a printer. In this case, the printing surface of the thermal transfer ink ribbon is brought into contact with a recording medium such as a sheet. FIG. 12 is a cross-sectional view of the inside of a printer to which a conventional thermal transfer ink ribbon cassette is attached, as seen in a direction perpendicular to the printing surface of the recording medium. In FIG. 12, reference numeral 1 denotes a thermal transfer ink ribbon cassette containing a thermal transfer ink ribbon (hereinafter also simply called a “ribbon”), reference numeral 2 denotes a thermal head which is an example of a printing means, reference numeral 3 denotes a platen roller which is a transportation means for transporting the ribbon 1 in the ribbon cassette 1 to the thermal head 2, and reference numeral 4 denotes a paper feed roller which is an example of a transportation means for transporting the recording medium (e.g., a sheet) in which an image is to be printed. The thermal transfer ink ribbon cassette 1 contains a thermal transfer ink ribbon 5. In this thermal transfer ink ribbon cassette 1, as shown in FIGS. 13(a) to 13(c), a thermal transfer ink ribbon 5 is contained between a PET film 6 as an example of a base film and a metal spool 7 (or a metal core around which the PET film 6 is wound) as an example of a supply reel. As shown in FIG. 13(a), in the thermal transfer ink ribbon cassette 1 which is thus constructed, the PET film 6 is wound around the supply reel 7 in the form of a roll. In FIG. 13(b), reference numeral 8 denotes a thermal transfer ink ribbon which is a ribbon to be used for the first time after the thermal transfer ink ribbon cassette 1 has been installed to a printer. Reference numeral 9 denotes a thermal transfer ink ribbon which is a ribbon to be used for the second time. The thermal transfer ink ribbons 8, 9 are wound around take-up reels 10, 11, respectively. Reference numeral 12 denotes a pair of release paper sheets that are inserted in order to separate the thermal transfer ink ribbon 8 from the thermal transfer ink ribbon cassette 1 after the ribbon has been used for the first time. Similarly, reference numeral 13 denotes a pair of release paper sheets that are inserted in order to separate the thermal transfer ink ribbon 9 from the thermal transfer ink ribbon cassette 1 after the ribbon has been used for the second time. Reference numeral 14 denotes a thermal transfer ink ribbon cassette lid which is opened when the thermal transfer ink ribbon cassette 1 is inserted into the printer, to take out the thermal transfer ink ribbon 9. Reference numeral 15 denotes a film leader for winding the thermal transfer ink ribbon 8. The film leader 15 is obtained by removing the thermal transfer ink ribbon 8 from the thermal transfer ink ribbon cassette 1 after the thermal transfer ink ribbon cassette 1 has been installed to the printer. Reference numeral 16 denotes a film leader for winding the thermal transfer ink ribbon 9. The film leader 16 is obtained by removing the thermal transfer ink ribbon 9 from the thermal transfer ink ribbon cassette 1 after the thermal transfer ink ribbon cassette 1 has been installed to the printer. Reference numeral 17 denotes a metal supply reel for taking out the thermal transfer ink ribbon 5 from the thermal transfer ink ribbon cassette 1 by rotating the supply reel 7 with a rotational force transmitted thereto. Reference numeral 18 denotes a lid opening and closing mechanism which is provided between the thermal head 2 and the PET film 6 so as to be able to separate the PET film 6 from the thermal head 2. The printer to which such a conventional thermal transfer ink ribbon cassette is attached is constructed as shown in FIG. 14. As shown in FIG. 14, a thermal transfer ink ribbon cassette 1 is placed on the thermal transfer ink ribbon cassette mount 19. Also, on the thermal transfer ink ribbon cassette mount 19, a paper feed roller 4 that is an example of a transportation means and a platen roller 3 that is an example of a transportation means are provided to face each other. Also, a thermal head 2 as an example of a printing means is installed above the platen roller 3 so that the PET film 6 in the thermal transfer ink ribbon cassette 1 comes into contact with the thermal head 2. In the conventional printer as constructed above, a color image can be printed by successively transporting the thermal transfer ink ribbons 8, 9 of respective colors from a thermal transfer ink ribbon cassette 1 to the platen roller 3 by rotating the platen roller 3. In the conventional printer as constructed above, the color image can be printed by successively transporting the thermal transfer ink ribbons 8, 9. For this purpose, as shown in FIGS. 15(a) and 15(b), a part of the PET film 6 in the thermal transfer ink ribbon cassette 1 is not used as the PET film 6 and is exposed to the outside. In this case, the PET film 6 exposed to the outside functions as a cover film for protecting the thermal transfer ink ribbons 8, 9 from dust or the like. Therefore, as shown in FIG. 14, it is necessary that the PET film 6 has a predetermined width of approximately 10 to 12 mm so that it can prevent the thermal transfer ink ribbon 8 from being exposed to the outside when the thermal transfer ink ribbon 8 is transported from the thermal transfer ink ribbon cassette 1 to the thermal head 2. Also, as shown in FIG. 16, there has been proposed such a printer that one thermal transfer ink ribbon cassette 1 containing a thermal transfer ink ribbon is placed on the thermal transfer ink ribbon cassette mount 19 and is removably attached to the printer so that color images can be successively printed by using the thermal transfer ink ribbons 8, 9. In this case, a color image can be printed by successively transporting the thermal transfer ink ribbons 8, 9 using one thermal transfer ink ribbon cassette 1. Thus, it is possible to reduce the number of thermal transfer ink ribbon cassettes. However, in such a printer, in addition to the thermal transfer ink ribbon cassette 1 containing the thermal transfer ink ribbon, an additional ink ribbon cassette (a separate-type cassette) for supplying an additional color ink ribbon has to be mounted in order to print color images. Thus, the printer becomes complicated in its structure. Also, when a printer is in use, an operator has to perform the operation of mounting the additional ink ribbon cassette. For this reason, a cassette mounting work takes a long time. In addition, when the cassette is not mounted at the correct position, an image cannot be printed on the recording medium. For this reason, it is necessary to mount the ink ribbon cassette with an extremely high degree of accuracy. It is also to be noted that when the ink ribbon cassette 1 is erroneously mounted to the wrong position, not only an image cannot be printed on the recording medium but also the cassette is wastefully consumed. Therefore, in order to solve such a problem, it is necessary to use a thermal transfer ink ribbon cassette for exclusive use for a thermal transfer printer.