Supercomputers are capable of increasingly more computations, and nodes forming them need to communicate even more efficiently with each other. The Message Passing Interface (MPI) proposes a communication model based on one-sided communications called the MPI Remote Memory Access (MPI-RMA). Thanks to these operations, applications can improve the overlap of communications with computations. However, one-sided communications are complex to write since they are subject to data races. This paper rethinks an existing on-the-fly data race detection algorithm for MPI-RMA programs by improving the storage of memory accesses in a Binary Search Tree using a new insertion algorithm based on fragmentation and merging algorithms. Thus, experimental results on real-life applications show that this new insertion algorithm improves the accuracy of the data race detection and can reduce the overhead of the analysis at runtime by a factor up to two.