The invention relates to a static copolymer of linear polyethylenimine that comprises two monomer units of the following formulas I and II, in which R1 is a hydrogen atom or a C1-C6 alkyl radical, R2 is a hydrogen atom, a C1-C6 alkyl, aryl or aralkyl group, wherein the alkyl group is a C1-C6 one, n is a number between 1 and 99% of the total monomers, m is a number between 1 and 99% of the total monomers, and advantageously m+n=100%. The invention also relates to complexes of this copolymer with a nucleic acid, and to the use thereof in in vivo, in vitro or ex vivo gene transfection.
