Method for producing 1,3-butadiene from a butanediol feedstock that comprises at least: a) A step for esterification of butanediol by a carboxylic acid to form the corresponding diester, fed by said butanediol feedstock and by a carboxylic acid feed comprising a carboxylic acid feedstock and the liquid pyrolysis effluent obtained from step b), and producing at least a carboxylic acid effluent and a diester effluent, implemented in reactive distillation in the presence of a homogeneous or heterogeneous acid catalyst, operated at a pressure of between 0.01 and 1 MPa; b) A step for pyrolysis of the diester effluent obtained from step a) comprising a reaction section and a separation section and producing at least a liquid pyrolysis effluent that comprises at least 50% by weight of carboxylic acid and a vapor pyrolysis effluent that comprises more than 90% by weight of butadiene, with said reaction section being operated at a temperature of between 500 and 650°C, the effluent of said reaction section being cooled to a temperature that is less than 100°C before feeding said separation section; c) A step for distillation fed by at least the carboxylic acid effluent obtained from step a), operated in a distillation column at a pressure that is at most equal to 1 MPa, with a temperature at the top of the column of between 0 and 110°C and a temperature at the bottom of the column of between 100 and 120°C, and producing an aqueous distillate comprising the by-products of step a) and step b), on the one hand, and a carboxylic acid residue, on the other hand; d) A step for drying the carboxylic acid that is fed at least by the carboxylic acid residue obtained from step c) and producing a water effluent and a carboxylic acid product that feeds step a). a) A step for esterification of butanediol by a carboxylic acid to form the corresponding diester, fed by said butanediol feedstock and by a carboxylic acid feed comprising a carboxylic acid feedstock and the liquid pyrolysis effluent obtained from step b), and producing at least a carboxylic acid effluent and a diester effluent, implemented in reactive distillation in the presence of a homogeneous or heterogeneous acid catalyst, operated at a pressure of between 0.01 and 1 MPa; b) A step for pyrolysis of the diester effluent obtained from step a) comprising a reaction section and a separation section and producing at least a liquid pyrolysis effluent that comprises at least 50% by weight of carboxylic acid and a vapor pyrolysis effluent that comprises more than 90% by weight of butadiene, with said reaction section being operated at a temperature of between 500 and 650°C, the effluent of said reaction section being cooled to a temperature that is less than 100°C before feeding said separation section; c) A step for distillation fed by at least the carboxylic acid effluent obtained from step a), operated in a distillation column at a pressure that is at most equal to 1 MPa, with a temperature at the top of the column of between 0 and 110°C and a temperature at the bottom of the column of between 100 and 120°C, and producing an aqueous distillate comprising the by-products of step a) and step b), on the one hand, and a carboxylic acid residue, on the other hand; d) A step for drying the carboxylic acid that is fed at least by the carboxylic acid residue obtained from step c) and producing a water effluent and a carboxylic acid product that feeds step a).