We show that the Alexander polynomial ΔL(t1,…,tμ) of a link L in S3 bounding a smooth compact oriented surface in B4 with μ connected components and Euler characteristic 1 is of the form p(t1,…,tμ)p(t1−1,…,tμ−1) for p ∈ ℤ[t1,…tμ], up to a unit and factors tk−1.