The　2　x　2　table　with　a　structural　zero　represents　a　common　scenario　in　clinical　trials　and　epidemiology,　characterized　by　a　specific　empty　cell.　In　such　cases,　the　risk　ratio　serves　as　a　vital　parameter　for　statistical　inference.　However,　existing　confidence　intervals,　such　as　those　constructed　through　the　score　test　and　Bayesian　methods,　fail　to　achieve　the　prescribed　nominal　level.　Our　focus　is　on　numerically　constructing　exact　confidence　intervals　for　the　risk　ratio.　We　achieve　this　by　optimally　combining　the　modified　inferential　model　method　and　the　h-function　method.　The　resulting　interval　is　then　compared　with　intervals　generated　by　four　existing　methods:　the　score　method,　the　exact　score　method,　the　Bayesian　tailed-based　method　and　the　inferential　model　method.　This　comparison　is　conducted　based　on　the　infimum　coverage　probability,　average　interval　length　and　non-coverage　probability　criteria.　Remarkably,　our　proposed　interval　outperforms　other　exact　intervals,　being　notably　shorter.　To　illustrate　the　effectiveness　of　our　approach,　we　discuss　two　examples　in　detail.