Reinforced rubber composition based at least (a) on an elastomeric matrix comprising non-halogenated natural rubber, (b) on a reinforcing filler, (c) on a polyimine compound corresponding to formula 1 or 2 below: in which: - R 4, R 5, R 6 and R 7, which are identical or different, are selected from alkyl groups having from 1 to 20 carbon atoms, cycloalkyl groups having from 5 to 24 carbon atoms, aryl groups having from 6 to 18 carbon atoms or aralkyl groups having from 7 to 25 carbon atoms; - R 1 and R 2, which are identical or different, are selected from the group consisting of alkylidenes having from 1 to 20 carbon atoms, cycloalkylidenes having from 5 to 24 carbon atoms, arylidenes having from 6 to 18 carbon atoms, aralkylidenes having from 7 to 25 carbon atoms and heterocycles, which are identical or different, having from 4 to 25 carbon atoms; - R 3 and R 8, which are identical or different, are selected from the group consisting of alkylidenes having from 1 to 20 carbon atoms, alkylidynes having from 1 to 20 carbon atoms, alkylylidynes having from 1 to 20 carbon atoms, cycloalkylidenes having from 5 to 24 carbon atoms, cycloalkylidynes having from 5 to 24 carbon atoms, cycloalkylylidynes having from 5 to 24 carbon atoms, arylidenes having from 6 to 18 carbon atoms, arylidynes having from 6 to 18 carbon atoms, arylylidynes having from 6 to 18 carbon atoms, aralkylidenes having from 7 to 25 carbon atoms, aralkylidynes having from 6 to 18 carbon atoms, aralkylylidynes having from 6 to 18 carbon atoms, and heterocycles, which are identical or different, having from 4 to 25 carbon atoms; - R 3 optionally comprises one or more heteroatom(s), chosen from O, N, S and Si; - m is equal to 1, 2 or 3; - n is equal to 1, 2 or 3. - R 4, R 5, R 6 and R 7, which are identical or different, are selected from alkyl groups having from 1 to 20 carbon atoms, cycloalkyl groups having from 5 to 24 carbon atoms, aryl groups having from 6 to 18 carbon atoms or aralkyl groups having from 7 to 25 carbon atoms; - R 1 and R 2, which are identical or different, are selected from the group consisting of alkylidenes having from 1 to 20 carbon atoms, cycloalkylidenes having from 5 to 24 carbon atoms, arylidenes having from 6 to 18 carbon atoms, aralkylidenes having from 7 to 25 carbon atoms and heterocycles, which are identical or different, having from 4 to 25 carbon atoms; - R 3 and R 8, which are identical or different, are selected from the group consisting of alkylidenes having from 1 to 20 carbon atoms, alkylidynes having from 1 to 20 carbon atoms, alkylylidynes having from 1 to 20 carbon atoms, cycloalkylidenes having from 5 to 24 carbon atoms, cycloalkylidynes having from 5 to 24 carbon atoms, cycloalkylylidynes having from 5 to 24 carbon atoms, arylidenes having from 6 to 18 carbon atoms, arylidynes having from 6 to 18 carbon atoms, arylylidynes having from 6 to 18 carbon atoms, aralkylidenes having from 7 to 25 carbon atoms, aralkylidynes having from 6 to 18 carbon atoms, aralkylylidynes having from 6 to 18 carbon atoms, and heterocycles, which are identical or different, having from 4 to 25 carbon atoms; - R 3 optionally comprises one or more heteroatom(s), chosen from O, N, S and Si; - m is equal to 1, 2 or 3; - n is equal to 1, 2 or 3.