  Let $R$ be a Noetherian ring, $M$ an Artinian $R$-module, $\p\in\Cos_RM$.
Then $\cograde_{R_{\p}}\Hom_{R}(R_{\p},M)=\inf\{i | \pi_{i}(\p,M)>0\}$ and
$$\pi_{i}(\p,M)>0\Rightarrow\cograde_{R_{\p}}\Hom_{R}(R_{\p},M)\leq
i\leq\fd_{R_{\p}}\Hom_{R}(R_{\p},M),$$ where $\pi_{i}(\p,M)$ is the $i$-th dual
Bass number of $M$ with respect to $\p$, the integer
$\cograde_{R_{\p}}\Hom_{R}(R_{\p},M)$ is the common length of any maximal
$\Hom_{R}(R_{\p},M)$-quasi co-regular sequence contained in $\p R_{\p}$, and
$\fd_{R_{\p}}\Hom_{R}(R_{\p},M)$ is the flat dimension of $R_{\p}$-module
$\Hom_{R}(R_{\p},M)$ (Theorem \ref{Thm:Main}). Besides, we also study the
relations among cograde, co-dimension and flat dimension of co-localization
module $\Hom_{R}(R_{\p},M)$.
