A method of treating cement clinker by grinding the clinker in a tubular mill while charging water, gypsum, and, optionally, also a water-reduction agent to the mill at the same time. The water has a pH of from about 9 to about 13. A microfill agent and/or a water-reduction agent is mixed with said the high pH-value water to form a slurry, which is added to the clinker during the grinding process together with microfill agent and/or water-reduction agent in a dry state. The high pH value of the water can be obtained by electrolysis.