For　the　traditional　method　to　computer　normal　form,　it　is　hard　to　carry　out　for　programming　and　reply　to　reduce　normal　forms　for　high　dimension.　The　authors　study　the　normal　forms　for　general　cases　of　the　four-dimensional　nonlinear　dynamical　systems.　For　Jordan　forms　of　the　linear　parts　with　two　double　zero　and　a　pair　of　pure　imaginary　eigenvalues,　with　the　aid　of　Maple　program　and　adjoint　operator,　the　authors　propose　the　computation　formula　and　coefficients　relations　with　original　system　for　seven　order　normal　form　with　four-dimensional　general　nonlinear　dynamical　systems　without　reducing　dimension　for　the　first　time.　The　introducing　improved　adjiont　operator　method　which　is　convenient　to　program　can　effectually　solve　high　dimension　problem.