In this paper, we construct a new family of harmonic morphisms $${\varphi:V^5\to\mathbb{S}^2}$$ , where V 5 is a 5-dimensional open manifold contained in an ellipsoidal hypersurface of $${\mathbb{C}^4\,=\,\mathbb{R}^8}$$ . These harmonic morphisms admit a continuous extension to the completion $${{V^{\ast}}^5}$$ , which turns out to be an explicit real algebraic variety. We work in the context of a generalization of the Hopf construction and equivariant theory.