In the field of business process management, adopting efficient building strategies can improve the quality of companies' business processes. The reuse of existing business processes or even fragments of them is a practical approach to build complete business processes or coarser-grained process fragments. In the present paper, we deal with the merge of a set of business process fragments for the construction of new complete processes. Our merge mechanism relies on a particular path matrix, that we call gateway path matrix. We use gateway path matrices to represent business process fragments to systematically compose shared components with individual ones. Moreover, our approach ensures that the resulting business process fragments subsume the behavior of initial ones and allows for adding new execution scenarios while controlling undesirable ones. In fact, we detect newly generated behaviors, and alert process designers of undesirable ones through behavioral constraints. We provide extensive experimental results derived from an implementation of our approach applied on a well-known industrial library of business process fragments