We observe independent random variable $Y_i sim N( heta_i,1), i=1,2,cdots,k$, and we are interested in detecting the treatment with the largest $ heta_i$. We consider a procedure which infers $ heta_{(k)} geq max heta_i (i eq(k))$ whenever $Y_{(k)} geq maxY_i+C (i eq(k))$. The maximum probability of a false inference is found, and it is shown that the inference can be made with the two-sample one-sided critical value for the usual error levels. The result also holds in the case of common unknown variance.