A method for the assisted recovery of petroleum in a deposit by means of the introduction of an aqueous solution of a hydrosoluble polymer into the deposit is characterized in that the aqueous solution is prepared by dissolving a polymer-based composition containing at least one hydrosoluble polymer, at least one radical capturing agent, and at least one sacrificial agent, in an aqueous solution subjected to a step of treatment with at least one deoxygenating agent, prior to the introduction of the polymer-based composition.