In [2] (or [3]) we have shown that every group $G$ possesses a uniquely determined subgroup $(V^*)^*(G)$ of the marginal subgroup $V^*(G)$ , which is minimal subject to being the image in $G$ of the marginal subgroup of some $\\cal V$-marginal extension of $G$, where $\\cal V$ is an arbitrary variety of groups defined by the set of laws $V$. In this talk, we answer the question that whether there exists a $\\cal V$-marginal extension of a group $G$ , with respect to the variety $\\cal V$, whose marginal subgroup is mapped onto $(V^*)^*(G)$. Two responses to this question is established in this note.

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