To increase the whiteness of pulp that is produced via the peroxide bleaching process and minimizes the undesirable release to the environment by reusing the filtrate.

Pulp is washed with a first washing solution in the first washing step, the washed pulp is fed from the first washing step to the peroxide- bleaching step 15, the bleached pulp is washed in the second washing step 16, the filtrate is formed, treated and transported to the first step where the treated filtrate is used as the washing solution. The filtrate is brought into close contact with an oxidative gas to oxidize the pollutants included therein. The ozone- bleaching step in included in before or after the peroxide-bleaching step and the ozone-containing gas is used for bleaching the pulp and the off gas including residual ozone is thereby formed. In a preferred embodiment, the residual ozone- including off gas is used as an oxidizing gas for the filtrate or can be used for removing the smell from other liquid flows in the pulp factory.