  Let $S=(a_1)\cdots(a_k)$ be a minimal zero-sum sequence over a finite cyclic
group $G$. The index conjecture states that if $k=4$ and $\gcd(|G|,6)=1$, then
$S$ has index $1$. In this paper we prove that if $S$ is singular then the
index of $S$ is $1$.
