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El-Zanati et al proved that for any 1-factorization $\mathcal{F}$ of thecomplete uniform hypergraph $\mathcal {G}=K_{rn}^{(r)}$ with $r\geq 2$ and$n\geq 3$, there is a rainbow 1-factor. We generalize their result and showthat in any proper coloring of the complete uniform hypergraph $\mathcal{G}=K_{rn}^{(r)}$ with $r\geq 2$ and $n\geq 3$, there is a rainbow 1-factor.

On the existence of a rainbow 1-factor in proper coloring of K_{rn}^{(r)}