Abstract.A Möbius triangulation is a triangulation on the Möbius band. A geometric realization of a map M on a surface Σ is an embedding of Σ into a Euclidean 3-space R 3 such that each face of M is a flat polygon. In this paper, we shall prove that every 5-connected triangulation on the Möbius band has a geometric realization. In order to prove it, we prove that if G is a 5-connected triangulation on the projective plane, then for any face f of G, the Möbius triangulation G − f obtained from G by removing the interior of f has a geometric realization.