A group testing procedure for the problem of identifying the sample minimum from a discrete uniform distribution in the minimal expected number of group tests is presented. A relation between the proposed procedure (PP) and other previously studied procedures (Sobel 1971; Hwang 1974, 1980) is shown to exist. Comparisons between the PP and other considered procedures are made and it is shown that the PP is uniformly better. A continuous case procedure is developed and is shown that under certain conditions the PP converges to it.