If the knot is the boundary of a singular disk which has the property that each self-intersecting component is an arc for which consists of two arcs in , one of which is interior, then is said to be a ribbon knot.

Every ribbon knot is a slice knot, and it is conjectured that every slice knot is a ribbon knot.

Knot , illustrated above, is a ribbon knot (Rolfsen 1976, p. 225).