Hypergroups that have at least one identity element and where each element has at least one inverse are called REGULAR hypergroup. In this regards, for a REGULAR hypergroup $H$, it is shown that there exists a correspondence between the set of all strongly REGULAR relations on $H$ and the set of all normal subhypergroups of $H$ containing $S_{\beta}$. More precisely, it has been proven that for every strongly REGULAR relation $\rho$ on $H$, there exists a unique normal subhypergroup of $H$ containing $S_{\beta}$, such that its quotient is a group, isomorphic to $H/\rho$. Furthermore, this correspondence is extended to a lattice isomorphism between them.