  A thin Lie algebras is a Lie algebra $L$, graded over the positive integers,
with its first homogeneous component $L_1$ of dimension two and generating $L$,
and such that each nonzero ideal of $L$ lies between consecutive terms of its
lower central series. All its homogeneous components have dimension one or two,
and the two-dimensional components are called diamonds. We prove that if the
next diamond past $L_1$ of an infinite-dimensional thin Lie algebra $L$ is
$L_k$, with $k>5$, then $[Lyy]=0$ for some nonzero element $y$ of $L_1$.
