To provide a rotary printing machine which does not generate a waste blank part in a sheet even when plates different in size are set for printing without replacing a plate cylinder.

A printing unit having the plate cylinder, an impression cylinder, a plate, and an ink roller as basic constituents is made a pair of printing units having the first printing unit and the second printing unit per one printing color. The driving source for the plate cylinders constituting both printing units is made a speed adjustable servo-motor which is provided independent of a driving source for a sheet conveying means. By adjusting/controlling the rotational speed of the servo-motor, the rotational speed of the plate cylinder is set and controlled to be synchronized with the traveling speed of the sheet during printing and to make a lapse of non-printing equal to a lapse of printing when printing is stopped. As a result, the printing surface and non-printing surface of the sheet are formed alternately in the same length during the operation of the first printing unit, and the printing surface is formed on the non- printing surface by the second printing unit.