Forbidden subgraphs in the norm graph

We show that the norm graph constructed in [J. Koll'{a}r, L. R'{o}nyai and T. Szab'o, Norm-graphs and bipartite Tur'{a}n numbers, Combinatorica, 16 (1996) 399–406] with $n$ vertices about $\frac{1}{2}{n}^{2-1\mathrm{/}t}$ edges, which contains no copy of $K_{t,(t-1)!+1}$, does not contain a copy of $K_{t+1,(t-1)!-1}$.