The　relative　risk　and　odds　ratio　are　widely　used　in　many　fields,　including　biomedical　research,　to　compare　two　treatments.　Extensive　research　has　been　done　to　infer　the　two　parameters　through　approximate　or　exact　confidence　intervals.　However,　these　intervals　may　be　liberal　or　conservative.　A　natural　question　is　whether　the　intervals　can　be　further　improved　in　maintaining　the　correct　confidence　coefficient　of　an　approximate　interval　or　shortening　an　exact　but　conservative　interval.　In　this　article,　when　two　independent　binomials　are　observed　we　offer　an　effort　to　improve　any　of　the　existing　intervals　by　applying　the　h-function　method.　In　particular,　if　the　given　interval　is　approximate,　then　the　improved　interval　is　exact;　if　the　given　interval　is　exact,　then　the　improved　interval　is　a　subset　of　the　given　interval.　This　method　is　also　applied　multiple　times　to　the　improved　intervals　until　the　final　resultant　interval　cannot　be　shortened　any　further.　To　demonstrate　the　effectiveness　of　the　method,　we　use　three　real　datasets　to　illustrate　in　detail　how　several　good　intervals　in　practice　are　improved.　Two　exact　intervals　are　then　recommended　for　estimating　each　of　the　two　parameters　in　different　scenarios.