To determine whether a chromosomal band is a fragile site rather than a spontaneous breakpoint, an essential step is to test the nonrandomness of breakage at the region. In this paper, the nonapplicability of the testing procedure introduced by Bohm et al. is discussed, and a new detection procedure is proposed. This new procedure considers the relations of one site with the others, and can be applied to tests of the nonrandomness of breakpoints under either the proportional probability model, or the equiprobability model. A data set for Chinese patients with colorectal carcinoma is analyzed as an illustration of the proposed method.