In a method for hydroformylating olefinically unsaturated compounds by means of a cobalt-based catalyst, used in a non-aqueous ionic liquid, liquid at a temperature below 100° C. and comprising at least one cation Q+ and at least one anion A−, said method comprising at least a stage of reaction under pressure and at least a stage of separation of the phases by decantation, recycling of the catalyst is improved: through the use of a ligand selected from among the Lewis bases, more particularly pyridine derivatives, and simultaneously through the addition of this ligand in a post-reaction stage. At the end of this process, the organic phase containing the reaction products can be recovered and the ionic liquid phase containing the catalyst can be recycled to the hydroformylation reactor.