2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/230281For any knot with genus one and unknotting number one, other than the figure-eight knot, we prove that there is exactly one way to unknot it by means of a crossing change. In the case of the figure-eight knot, we prove that there are precisely two unknotting crossing changes. The proof uses sutured manifold theory and an analysis of the arc complex of the once-punctured torus.17 pages, 11 figures; v2 corrects an error in Section 4; v3 is the final version. To appear in Commentarii Mathematici HelveticiGeometric Topology57M25; 57N10text