Method for Kraft cooking of lignocellulose material with low-sulphide alkaline lyes in the production of pulp with direct incorporation of dihydroxyanthracene disodium saltinto the digester. The additive is obtained in parallel with the cooking and is incorporated into the digester of the lignocellulose material in the most active soluble form thereof (dihydroxyanthracene disodium salt) during the extended delignification step, at a time prior to the critical conditions of degradation of the cellulose, simultaneously allowing a reduction in sulphide content. Pulps are obtained that have a low lignin content (low Kappa indices) and good mechanical properties (low degradation of the cellulose polymer).