Forbidden subgraphs in the norm graph

We show that the norm graph constructed in [J. Kollár, L. Rónyai and T. Szabó, Norm-graphs and bipartite Turán numbers, Combinatorica, 16 (1996) 399--406] with $n$ vertices about $\frac{1}{2}n^{2-1/t}$ edges, which contains no copy of $K_{t,(t-1)!+1}$, does not contain a copy of $K_{t+1,(t-1)!-1}$.

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