Abstract: Borohydride metallocene complex of lanthanide, preparation process, catalytic system incorporating borohydride metallocene complex, process for copolymerization of olefins employing catalytic system. The complex corresponds to one or other of formulae A and B: where, in A, two ligands Cp1, Cp2, each composed of a cyclopentadienyl group, are connected to the lanthanide Ln, such as Nd, and where, in B, a ligand molecule, composed of two cyclopentadienyl groups Cp1, Cp2 connected to one another via a bridge P of formula MR1R2, M is an element from group IVa, and R1 and R2, which are identical or different, represent an alkyl group comprising from 1 to 20 carbon atoms, is connected to the lanthanide Ln, L is alkali metal, N is molecule of a complexing solvent, x is integral or non-integral number?0, p is integer?than 1 and y is integer?0.