  We propose a modification to the Lie algebra $S$-expansion method. The
modification is carried out by imposing a condition on the $S$-expansion
procedure, when the semigroup is given by a cyclic group of even order. The
$S$-expanded algebras are called $S_{H}$-expanded algebras where $S=Z_{2n}$.
The invariant tensors for $S_{H}$-expanded algebras are calculated and the dual
formulation of $S_{H}$-expansion procedure is proposed. We consider the
$S_{H}$-expansion of the five-dimensional $AdS$ algebra and its corresponding
invariants tensors are found. Then a Chern-Simons Lagrangian invariant under
the five-dimensional $AdS$ algebra $S_{H}$-expanded is constructed and its
relationship to the general relativity is studied.
