A process for producing a thiourea dioxide fluid by mixing thiourea and a peroxide, or thiourea, a peroxide and a reaction catalyst, or thiourea, a peroxide, a reaction catalyst and a chelating agent, in the absence or presence of pulp and a process for bleaching pulp by the use of the thiourea dioxide fluid produced by the above process economically advantageously with a small chemicals loss and by small consumption of energy.