In this note, we give a new proof of the existence of an open book decomposition for a closed non-orientable 3-manifold. This open book decomposition is analogous to a planar open book decomposition for a closed orientable 3-manifold. More precisely, in this note, we give an open book decomposition of a given closed non-orientable 3-manifold with the pages punctured Möbius bands. We also give an algorithm to determine the monodromy of this open book. © Glasgow Mathematical Journal Trust 2019.