Summary: G. Kalai and D. J. Kleitman [Bull. Am. Math. Soc., New Ser. 26, No. 2, 315–316 (1992; Zbl 0751.52006)] established the bound \(n^{\log(d) + 2}\) for the diameter of a \(d\)-dimensional polyhedron with \(n\) facets. Here, we improve the bound slightly to \((n-d)^{\log(d)}\).