A combination of a thermal printer and an invertible ribbon cassette has a mechanism for preventing a portion of the inked ribbon extending between a supply core and a take-up core of the ribbon cassette from shifting in the direction perpendicular to the longitudinal direction of the inked ribbon with respect to a printing head. The mechanism includes a substantially planar surface of a platen, and a printing head is urged against the planar surface of the platen through the inked ribbon portion and a sheet to which solid ink in the area on the inked ribbon portion is transferred by the printing head. The width of that area on the inked ribbon portion in the widthwise direction of the inked ribbon is at most equal to a half of the width of the inked ribbon. Alternatively, the mechanism includes a detector mechanism operative in response to the variation in diameter of the inked ribbon wound on the supply core for applying a variable back tension in the reverse direction to the tension acting on the inked ribbon portion by the take-up core.