On the cycles separating the system of $m$ hypersurfaces in the neighbourhood of the point in $\mathbb C^n$

It is known, that any $n$-cycle on a Stein manifold of dimension $n$, which topologically separates $n$ hypersurfaces, is homologous to the linear combination of the local cycles in the discrete intersection of the hypersurfaces. In this paper we consider the case when $m>n$. Particulary, we proof that in the local case, if $m=n+1$, such cycles is also related with discrete intersection of $n$-subsets of hiperfaces.