Let $(R,\fm)$ be a commutative Noetherian local ring and $M$, $N$ two non-zero finitely generated $R$-modules with $\pd(M)=n<\infty$ and $\Dim(N)=d$. In this paper, we show that if the top generalized local cohomology module $H_{\fm}^{n+d}(M,N)\neq 0$, then the following statements are equivalent: \begin{itemize} \item[(i)] $\Ann(0:_{H_{\fm}^d(N)}\fp)=\fp$ for all $\fp\in\V(\Ann(H_{\fm}^d(N)))$; \item[(ii)] $\Ann(0:_{H_{\fm}^{n+d}(M,N)}\fp)=\fp$ for all $\fp\in\V(\Ann(H_{\fm}^{n+d}(M,N)))$. \end{itemize}
