A　framework　to　systematically　decouple　high　order　elliptic　equations　into　a　combination　of　Poisson-type　and　Stokes-type　equations　is　developed.　The　key　is　to　systematically　construct　the　underling　commutative　diagrams　involving　the　complexes　and　Helmholtz　decompositions　in　a　general　way.　Discretizing　the　decoupled　formulation　leads　to　a　natural　superconvergence　between　the　Galerkin　projection　and　the　decoupled　approximation.　Examples　include　but　are　not　limited　to　the　primal　formulations　and　mixed　formulations　of　the　biharmonic　equation,　fourth　order　curl　equation,　and　triharmonic　equation.　As　a　byproduct,　Helmholtz　decompositions　for　many　dual　spaces　are　obtained.