 Is any one-sorted structure \(\mathcal{E}\) of signature \(\Sigma ^{\ast}\) convertible into a many-sorted one of signature \(\Sigma\)? The answer is negative, as there are two problems that could stop the conversion: the first one is that in a many-sorted structure all the universes should be nonempty and our idea is to take for each sort \(i\) the unary relation \(Q_{i}^{\mathcal{E}}\) as universe of sort \(i\) and so we need it to be nonempty; the second difficulty concerns operation symbols with \(\Rank(f)=\langle i_{1},\ldots i_{n},i_{0}\rangle\) whose interpretation in structure \(\mathcal{E}\) is just an n-ary function, but we need the values of \(f^{\mathcal{E}}\upharpoonright (Q_{i_{1}}^{\mathcal{E}}\times \ldots \times Q_{i_{n}}^{\mathcal{E}})\) to be in \(Q_{i_{0}}^{\mathcal{E}}\).