Normal　form　theory　is　robust　and　useful　for　direct　bifurcation　and　stability　analysis　of　nonlinear　differential　equations　in　real　engineering　problems.　This　paper　develops　a　new　computation　method　for　obtaining　a　significant　refinement　of　the　normal　forms　for　high　dimensional　nonlinear　systems.　In　the　theoretical　model　for　the　nonlinear　oscillation　of　a　composite　laminated　piezoelectric　plate,　the　computation　method　is　applied　to　compute　the　coefficients　of　the　normal　forms　for　the　case　of　one　double　zero　and　a　pair　of　pure　imaginary　eigenvalues.　The　algorithm　is　implemented　in　Maple　V　and　the　normal　forms　of　the　averaged　equations　and　their　coefficients　for　nonlinear　oscillations　of　the　composite　laminated　piezoelectric　plate　under　combined　parametric　and　transverse　excitations　are　calculated.