In the present work, we propose an approach to merge business process fragments in order to facilitate the reuse of fragments in business process designs. The approach relies on the so-called adjacency matrices. Typically used to handle graphs, this concept represents a new way to systematically merge fragments through their corresponding matrices. At the same time, fragments merging must keep the behavior of the original fragments consisting of their execution scenarios and rule out undesirable ones that may be generated during the merge task. Indeed, such behaviors probably lead to process execution blocking. The proposed approach has been implemented and tested on a collection of fragments and experimental results are provided