This　article　explores　the　subharmonic　orbits　of　a　four-dimensional　degenerate　resonance　non-autonomous　system.　The　well-known　subharmonic　Melnikov　method　is　improved　in　this　paper.　Suppose　the　unperturbed　system　is　a　two-degree-of-freedom　decoupled　Hamiltonian　system　and　possesses　a　family　of　periodic　orbits.　The　important　issue　is　the　persistence　of　the　periodic　orbits　after　periodic　perturbations.　In　order　to　solve　this　problem,　we　propose　a　four-dimensional　subharmonic　Melnikov　function　based　on　periodic　transformations　and　Poincar,　map.　Then,　a　main　theorem,　which　can　be　used　to　check　the　existence　of　the　periodic　orbits　for　the　four-dimensional　degenerate　resonance　system,　is　presented　and　proved　by　using　the　implicit　function　theorem.　In　order　to　verify　the　validity　and　applicability　of　the　improved　subharmonic　Melnikov　method,　we　apply　it　to　investigate　the　subharmonic　orbits　of　a　honeycomb　sandwich　plate.　The　theoretical　result　shows　that　the　subharmonic　orbits　of　period　2T　can　exist　under　certain　conditions.　Numerical　simulations　are　carried　out　to　verify　the　analytical　predictions.　It　is　found　that　the　subharmonic　orbits　for　the　honeycomb　sandwich　plate　do　exist　based　on　the　results　of　numerical　simulations.