Method for preparing a polymer based on a polyhydroxylated fatty acid, comprising, successively, steps of: - preparation of a reaction medium by bringing together: - a monomer selected from polyhydroxylated fatty acids comprising an hydroxyl group at the ω position and esters of a polyhydroxylated fatty acid comprising an hydroxyl group at the ω position and of an alcohol with a linear or branched, saturated or unsaturated, optionally substituted, aliphatic chain, said aliphatic chain including from 1 to 18 carbon atoms; or a mixture of hydroxylated fatty acids and/or esters of a hydroxylated fatty acid and of an alcohol with a linear or branched, saturated or unsaturated, optionally substituted, aliphatic chain, said aliphatic chain including from 1 to 18 carbon atoms, said mixture containing at least 20% by weight of said monomer with respect to the total weight of said mixture, - with a polyol different from said monomer and where appropriate different from said hydroxylated fatty acids and/or said esters of said mixture, said reaction medium being free of catalyst, - and heating of said reaction medium to carry out the copolymerisation of said monomer and of said polyol and the crosslinking of the polymer thus formed, characterized in that at least an initial phase of the heating step is carried out under reduced pressure, at a pressure comprised between 0 and 900 mbar. - preparation of a reaction medium by bringing together: - a monomer selected from polyhydroxylated fatty acids comprising an hydroxyl group at the ω position and esters of a polyhydroxylated fatty acid comprising an hydroxyl group at the ω position and of an alcohol with a linear or branched, saturated or unsaturated, optionally substituted, aliphatic chain, said aliphatic chain including from 1 to 18 carbon atoms; or a mixture of hydroxylated fatty acids and/or esters of a hydroxylated fatty acid and of an alcohol with a linear or branched, saturated or unsaturated, optionally substituted, aliphatic chain, said aliphatic chain including from 1 to 18 carbon atoms, said mixture containing at least 20% by weight of said monomer with respect to the total weight of said mixture, - with a polyol different from said monomer and where appropriate different from said hydroxylated fatty acids and/or said esters of said mixture, said reaction medium being free of catalyst, - a monomer selected from polyhydroxylated fatty acids comprising an hydroxyl group at the ω position and esters of a polyhydroxylated fatty acid comprising an hydroxyl group at the ω position and of an alcohol with a linear or branched, saturated or unsaturated, optionally substituted, aliphatic chain, said aliphatic chain including from 1 to 18 carbon atoms; or a mixture of hydroxylated fatty acids and/or esters of a hydroxylated fatty acid and of an alcohol with a linear or branched, saturated or unsaturated, optionally substituted, aliphatic chain, said aliphatic chain including from 1 to 18 carbon atoms, said mixture containing at least 20% by weight of said monomer with respect to the total weight of said mixture, - with a polyol different from said monomer and where appropriate different from said hydroxylated fatty acids and/or said esters of said mixture, - and heating of said reaction medium to carry out the copolymerisation of said monomer and of said polyol and the crosslinking of the polymer thus formed, characterized in that at least an initial phase of the heating step is carried out under reduced pressure, at a pressure comprised between 0 and 900 mbar. <EOS>