Abstract. An embedding M of a graph G is said to be regular if and only if for every two triples (v₁,e₁,f₁) and (v₂,e₂,f₂), where e_i is an edge incident with the vertex v_i and the face f_i, there exists an automorphism of M which maps v₁ to v₂, e₁ to e₂ and f₁ to f₂. We show that if n is not congruent to 0 modulo 8 then there is, up to ismorphism, precisely one regular Hamiltonian embedding of K_n,n in an orientable surface, and that if n is congruent to 0 modulo 8 then there are precisely two such embeddings. We give explicit construction for these embeddings as lifts of spherical embeddings of dipoles.