Investigate　of　hypernormal　form　(the　simplest　normal　form　and　the　unique　normal　form)　for　highdimensional　vector　fields　which　have　applied　in　practical　engineering　can　provide　guidance　for　the　principle　of　industry　design　and　the　theory　of　standardization　in　reality.　In　this　paper,　based　on　the　method　combined　new　grading　function　with　multiple　Lie　brackets,　we　investigated　the　reduction　hypernormal　form　problem　for　a　class　of　four-dimensional　vector　fields　with　linear　part　has　two　pairs　of　pure　imaginary　eigenvalues.　With　the　aid　of　Maple　and　new　expressions　of　block　matrices,　we　obtained　the　hypernormal　form　at　quintic　truncated　and　proved　that　was　a　unique　one　under　certain　condition.　As　an　application,　we　studied　the　simply　supported　honeycomb　sandwich　plate　dynamics　model　and　obtained　the　hypernormal　form　at　quintic　truncated.　©　2013　IFSA.