Cyclic, diagonal and facial colorings—a missing case

In [D. Král’, T. Madaras, R. Škrekovski, Cyclic, diagonal and facial colorings, European J. Combin. 26 (2005) 473–490], we established that every planar graph has a coloring with eight colors such that no two vertices joined by a facial walk of length one or two receive the same color. It turned out that the analysis of one of the cases in our proof is incomplete. We provide a completed analysis in this note.