The well known Wald test comparing the means of two normal samples with unequal variances is of the form: $|{{\bar x - \bar y} / {s_2 }}| \geqq \varphi ({{s_1 } / {s_2 }})$ (critical zone). A. Wald constructed the function $\varphi $ for which the test is approximately similar with respect to $\sigma _1 $ and $\sigma _2 $. The present article shows that even under mild conditions on the function $\phi $, Wald’s exact similar test is impossible.