The present invention relates to a catalytic system based at least on a rare-earth metallocene having, as ligand, a molecule consisting of two groups selected from the group consisting of cyclopentadienyl groups substituted at least at position 2 and 5, substituted fluorenyl groups, the unsubstituted fluorenyl group and indenyl groups substituted at least at position 2, and joined by a bridge. The catalytic system makes it possible to attain copolymers of ethylene and of 1,3-butadiene comprising cyclic units containing 6 carbon atoms, with an insertion of the butadiene monomer into the copolymer in the form of the trans-1,4 unit that represents more than 50 mol% of the vinyl (1,2), 1,4 and cyclic units.