To improve printing quality and productivity by a method wherein dampening water is exchanged at a proper period.

In each of printing units 2A-2D, a water supplying device for supplying dampening water 25 and an ink arrangement device for supplying ink to a plate cylinder 3 are provided. To the water cistern 8 of the water supplying device, the dampening water 25 in a tank 26 is supplied by means of a pump 28 through a water supply pipe 29 and pipings 30A-30D. A calcium ion detector 40 is being immersed in the dampening water 25 in the tank 26 under the state where the calcium ion detector 40 is connected with an alarming device 41 and a printing quality controlling device 42. When the detected density of detected calcium ion exceeds a pre-set value, an alarming sound is emitted from the alarming device 41.