  A harmonious coloring of a $k$-uniform hypergraph $H$ is a vertex coloring
such that no two vertices in the same edge have the same color, and each
$k$-element subset of colors appears on at most one edge. The harmonious number
$h(H)$ is the least number of colors needed for such a coloring.
  The paper contains a new proof of the upper bound $h(H)=O(\sqrt[k]{k!m})$ on
the harmonious number of hypergraphs of maximum degree $\Delta$ with $m$ edges.
We use the local cut lemma of A. Bernshteyn.
