Identification of fragile sites is a way to investigate the genetic abnormalities that are the hallmark of cancer and play an important role in carcinogenesis. Manifestation of nonrandom breakage at a chromosome band is an essential criterion for determination of the fragility of the band. In this article, a new detection procedure is proposed. This new procedure takes the relationship of one site with the others into consideration and can be applied to tests of the randomness of breakpoints under either the proportional probability model (PPM) or the equiprobability model (EPM). The procedure can form a grouping structure that classifies all sites into several clusters. It is applied to identification of fragile sites for a real data set for Chinese patients with colorectal carcinoma for illustration of the proposed method.