  A longstanding avenue of research in orientable surface topology is to create
and enumerate collections of curves in surfaces with certain intersection
properties. We look for similar collections of curves in non-orientable
surfaces. A surface is non-orientable if and only if it contains a M\"obius
band. We generalize a construction of Malestein-Rivin-Theran to non-orientable
surfaces to exhibit a lower bound for the maximum number of curves that
pairwise intersect 0 or 1 times in a generic non-orientable surface.
