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This paper proves a result: Suppose that $$X$$ is strongly normal and $$\overline X=[-1,1]$$. If $$f\in C[-1,1]$$ satisfies $$\| H_n(X,f)-f\| =\circ (n^{-1})$$ then $$f=constant$$, where $$H_n(X,f)$$ is the Hermite approximation interpolation of $$f$$ on the nodes $$X$$. But this result is only a direct consequence of Theorem 8 in Reference [3] of the paper ([Some notes on Hermite-Fejér type interpolation, Approximation Theory Appl. 7, No. 4, 28-39 (1991; Zbl 0757.41006)] given by the reviewer.