Recent researches have proposed to retrieve relevant fragments out from whole business processes to build new ones. Although they avoid building business processes from scratch, this task has been performed independently for each process, thus, making resulting fragments handling complicated. In this paper, we propose to merge some given business process fragments in order to facilitate the fragment-based business process design. At the same time, the obtained fragment must keep the behavior of original fragments so as to avoid paths execution blockage while the obtained fragments are integrated as part of a complete process. Our approach presents a systematic merge revolving around the so-called adjacency matrices. Typically used to handle graphs, this mechanism is adapted to business process fragments. We also present some rules to provide the obtained fragments with the behavior of original fragments and avoid inconsistent behaviors that were newly added after the merge