In this paper, we study 1-homoclinic loop bifurcations on a non-orientable 2-manifold: the Möbius band. The techniques for studying bifurcating dynamics of the 1-homoclinic loop on this manifold are similar to those for a figure-eight loop in the plane. We adapt the techniques revealed in a paper by Jebrane and Mourtada (1994 Cyclicité finie des lacets doubles non triviaux 7 1349-65) covering the subject: we are able, studying the 2-return map where it exists, to give an explicit bound for the cyclicity of the 1-homoclinic loop for all arbitrary finite codimensions. The key element is a blow-up. A simple corollary is to prove the completeness of the bifurcation diagram given by Chow et al (1990 Homoclinic bifurcation at resonant eigenvalues, J. Dyn. Diff. Equ. 2 177-244).