The handle slide operation was originally defined for ribbon graphs. Later, I. Moffatt and E. Mphako-Bandab extended this concept to \(\Delta \) -matroids. They showed that, using a \(\Delta \) -matroid analogue of handle slides, every binary \(\Delta \) -matroid in which the empty set is feasible can be expressed in a canonical form. This form is analogous to the canonical representation of one-vertex maps on a surface. We provide a canonical form for binary \(\Delta \) -matroids without any restriction on the feasibility of the empty set.
