Multi-head　attention　(MA),　which　allows　the　model　to　jointly　attend　to　crucial　information　from　diverse　representation　subspaces　through　its　heads,　has　yielded　remarkable　achievement　in　image　captioning.　However,　there　is　no　explicit　mechanism　to　ensure　MA　attends　to　appropriate　positions　in　diverse　subspaces,　resulting　in　overfocused　attention　for　each　head　and　redundancy　between　heads.　In　this　paper,　we　propose　a　novel　Intra-　and　Inter-Head　Orthogonal　Attention　(I(2)OA)　to　efficiently　improve　MA　in　image　captioning　by　introducing　a　concise　orthogonal　regularization　to　heads.　Specifically,　Intra-Head　Orthogonal　Attention　enhances　the　attention　learning　of　MA　by　introducing　orthogonal　constraint　to　each　head,　which　decentralizes　the　object-centric　attention　to　more　comprehensive　content-aware　attention.　Inter-Head　Orthogonal　Attention　reduces　the　heads　redundancy　by　applying　orthogonal　constraint　between　heads,　which　enlarges　the　diversity　of　representation　subspaces　and　improves　the　representation　ability　for　MA.　Moreover,　the　proposed　I(2)OA　is　flexible　to　combine　with　various　multi-head　attention　based　image　captioning　methods　and　improve　the　performances　without　increasing　model　complexity　and　parameters.　Experiments　on　the　MS　COCO　dataset　demonstrate　the　effectiveness　of　the　proposed　model.