The invention relates to a method for precipitating calcium carbonate, in which method calcium hydroxide is introduced to a fiber suspension containing cellulose-containing fibers, the calcium hydroxide is allowed to attach onto the surfaces of fibers for a pre-determined time, and the aqueous suspension of calcium hydroxide and fibers is brought into contact with carbon dioxide for precipitating the calcium carbonate. The invention also relates to a corresponding system for precipitating calcium carbonate in connection with cellulose-containing fibers. In addition, the invention relates to a fibrous product, which comprises pulp material produced by said method and comprising calcium carbonate.