In　this　paper,　we　mainly　locus　on　the　hypernormal　form　for　a　class　of　four-dimensional　nilpotent　vector　fields,　and　the　results　are　applied　to　simplify　the　practical　engineering　models　in　the　high-dimensional　nonlinear　dynamics.　We　improve　and　develop　the　further　reduction　theory　of　the　normal　form　proposed　by　Sanders,　Baider　and　KOW,　and　based　on　the　method　of　linear　grading　function,　multiple　Lie　bracket　and　the　new　notations　for　block　matrices,　we　obtain　the　three　order　and　the　live　order　hypernormal　form,　respectively,　and　then　the　results　are　applied　to　simplify　the　circular　truss　antenna　models.　The　introduction　of　the　new　notations　for　block　matrices　gives　a　new　method　for　dealing　with　the　calculation　of　big　size　block　matrices,　which　brings　conveniences　for　the　later　research.　©　Journal　of　Dynamics　and　Control.　All　rights　reserved.