Given a link projection [Formula: see text] and a link [Formula: see text], it is natural to ask whether it is possible that [Formula: see text] is a projection of [Formula: see text]. Taniyama answered this question for the cases in which [Formula: see text] is a prime knot or link with crossing number at most five. Recently, Takimura settled the issue for the knot [Formula: see text]. We answer this question for the case in which [Formula: see text] is the link [Formula: see text].