The invention can be summarized as follows. There is provided a method of bleaching chemical pulp comprising the steps of exposing chemical pulp to a chemical bleaching state to produce a partially bleached pulp and treating the partially bleached pulp with a thermophilic, alkalophilic xylanase in an alkaline extraction stage at pH of 8 to 14. The method may be performed in a mill and may form part of a more complex pulp bleaching process. The invention also relates to the use of a thermophilic, alkalophilic xylanase in an alkaline extraction stage of a pulp bleaching process in a mill.