The efficiency of path sampling simulations can be improved considerably using the approach of path swapping. For this purpose, we devise a new algorithmic procedure based on the transition interface sampling technique. In the same spirit of parallel tempering, paths between different ensembles are swapped, but the role of temperature is here played by the interface position. We test the method on the denaturation transition of DNA using the Peyrard-Bishop-Dauxois model. We find that the new algorithm gives a reduction of the computational cost by a factor of 20.