The method is for the improved oxygen delignification of cellulose pulp with a medium consistency of 8-16%. The fraction of dissolved oxygen can be maintained at a high level throughout the process by the use of high pressure, greater than 15.0 bar, and by repeated agitative mixing while maintaining the high pressure. A fraction just over 20% of the total oxygen added is dissolved in the fluid phase such that the amount of oxygen in the fluid phase is maintained at a high level throughout the complete high-pressure section. This means that the amount of oxygen that is dissolved in the fluid phase and that penetrates the cellulose fibers can be maintained at an optimal high level throughout the process for improved delignification of the cellulose.