  We show that the equivariant and non-equivariant non-orientable 4-genus of
p-periodic knots may differ, for any choice of p>1. Similar results have
previously been obtained for the smooth 4-genus and non-orientable 3-genus of a
periodic knot. These stand in contrast to Edmods' acclaimed result by which the
equivariant and non-equivariant Seifert genus of a periodic knot agree.
