Abstract Given a four-dimensional manifold ( M , g ) , we study the existence of a conformal metric for which the Q-curvature, associated to a conformally invariant fourth-order operator (the Paneitz operator), is constant. Using a topological argument, we obtain a new result in cases which were still open. To cite this article: Z. Djadli, A. Malchiodi, C. R. Acad. Sci. Paris, Ser. I 340 (2005).