Linear or branched polyurethane resin based on fatty polyester, in particular based on alkyd resin, characterized in that it is obtained from at least one hydroxylated fatty polyester A), with: - said polyester A) being the product of reaction of a) an alcohol component with b) an acid component, which acid component b) comprises b1) at least one fatty acid, said fatty acid being chosen from b1.1) at least one oxidizable fatty monoacid and/or polyacid, comprising at least one oxidizable unsaturation or b1.2) at least one non-oxidizable fatty monoacid and/or polyacid or b1.3) at least one mixture of fatty acids b1.1) and b1.2) and said component b) also comprising b2) rosin and/or rosin derivatives bearing at least one carboxylic acid function, said rosin and/or derivatives b2) representing from 30% to 85%, preferably from 35% to 75%, more preferentially from 40% to 75% and even more preferentially from 45% to 75% by weight relative to the total weight of A) - optionally, said polyester A) having a zero oil length (0%) or an oil length of between 0 and 60%, preferably from 0 to 50% and more preferentially from 0 to 40% - optionally, said polyester A) having a weight ratio of oxidizable fatty acids (monoacids) b1.1) relative to the overall fatty acids b1.1) + b1.2) of 0 or greater than 0 and ranging up to 1 and with said resin being the product of reaction of said polyol polyester A) with: B) at least one diol comprising an acid function, chosen from carboxylic, sulfonic, phosphonic or phosphinic (preferably carboxylic), sulfonic or phosphonic and more preferentially carboxylic, said acid function optionally being partially or totally neutralized in salt form with a weak base, preferably chosen from amines and phosphines and C) at least one polyisocyanate, of functionality ranging from 2 to 3, preferably diisocyanate, more preferentially cycloaliphatic. - said polyester A) being the product of reaction of a) an alcohol component with b) an acid component, which acid component b) comprises b1) at least one fatty acid, said fatty acid being chosen from b1.1) at least one oxidizable fatty monoacid and/or polyacid, comprising at least one oxidizable unsaturation or b1.2) at least one non-oxidizable fatty monoacid and/or polyacid or b1.3) at least one mixture of fatty acids b1.1) and b1.2) and said component b) also comprising b2) rosin and/or rosin derivatives bearing at least one carboxylic acid function, said rosin and/or derivatives b2) representing from 30% to 85%, preferably from 35% to 75%, more preferentially from 40% to 75% and even more preferentially from 45% to 75% by weight relative to the total weight of A) - optionally, said polyester A) having a zero oil length (0%) or an oil length of between 0 and 60%, preferably from 0 to 50% and more preferentially from 0 to 40% - optionally, said polyester A) having a weight ratio of oxidizable fatty acids (monoacids) b1.1) relative to the overall fatty acids b1.1) + b1.2) of 0 or greater than 0 and ranging up to 1 B) at least one diol comprising an acid function, chosen from carboxylic, sulfonic, phosphonic or phosphinic (preferably carboxylic), sulfonic or phosphonic and more preferentially carboxylic, said acid function optionally being partially or totally neutralized in salt form with a weak base, preferably chosen from amines and phosphines and C) at least one polyisocyanate, of functionality ranging from 2 to 3, preferably diisocyanate, more preferentially cycloaliphatic.