Let \(H\) be a hypergroupoid and \(n \in \mathbb{N}^*\). Let \(\gamma\) be a grouping of the indices \(\{1,\dots,n\}\) respecting their order. If \(z_ 1,z_ 2,\dots,z_ n\) are elements of \(H\) we denote by \(\displaystyle\prod^ n_{i=1}{^{(\gamma)} z_ i}\) the product of these elements according to \(\gamma\). Define on \(H\) a relation \(\Delta\) by: \(x \Delta y\) if and only if there exist \(n \in \mathbb{N}^*\), \((z_ 1,\dots,z_ n) \in H^ n\) and two different groupings \((\gamma)\) and \((\gamma')\) of the indices \(\{1, \dots,n\}\) such that \(x \in \displaystyle\prod^ n_{i=1}{^{(\gamma)} z_ i}\) and \(y\in\displaystyle\prod^ n_{i=1}{^{(\gamma')} z_ i}\). The relation \(\Delta\) is reflexive and symmetric. In fact \(\Delta\) is a generalisation to hypergroupoids of a similar relation \(\mathcal A\) introduced by \textit{M. Koskas} for groupoids [J. Math. Pures Appl., IX. Sér. 49, 155-192 (1970; Zbl 0194.02201)]. Denote by \(\Delta^*\) the transitive closure of \(\Delta\). It is shown that \(\Delta^*\) is a strongly regular equivalence on \(H\). The main result establishes that in a quasi-hypergroup \(\Delta = \Delta^*\). Some connections between the relations \(\Delta\) and \(\beta\) are also obtained [see \textit{P. Corsini}, Prolegomena of Hypergroup Theory (Aviani Editore, 1993; Zbl 0785.20032)].