A previous result [F. K. Hwang, Tamkang J. Math., 2 (1971), pp. 39–44] showed that a minimax group testing algorithm to find d defectives in n items is to test each item individually for $d\geqq 0.5n$. In this paper we improve this result by proving that individual testing is minimax for $d\geqq 0.4n$. We also conjecture that the same is true for $d\geqq \frac{1}{3}n$. On the other hand, we prove that individual testing is not minimax for $d < \frac{1}{3}n$.