  Let $(N,L)$ be a pair of finite dimensional nilpotent Lie algebras and $N$
admits a complement $K$ in $L$ such that $\dim N=n$ and $\dim K=m$. Let
$s(N,L)=\frac{1}{2}(n-1)(n-2)+1+(n-1)m-\dim \M(N,L)$, where $\M(N,L)$ denotes
the multiplier of the pair $(N,L)$. The aim of this paper is to classify all
pairs of finite dimensional nilpotent Lie algebras $(N,L)$, for which
$s(N,L)=6,7$.
