In　this　paper,　a　new　explicit　expression　of　the　geometrically　nonlinear　finite　element　method　was　developed　on　the　complementary　energy　principle　for　the　large　displacement　and　large　rotation　problem　on　the　basis　of　the　concept　of　base　forces　as　fundamental　variables.　The　complementary　energy　of　an　element　under　large　deformation　case　is　divided　into　the　deformation　part　and　rotation　part.　The　formulations　of　the　control　equations　for　the　base　forces　finite　element　method　are　obtained　using　the　Lagrange　multiplier　method,　and　an　explicit　displacement　formulation　of　nodes　is　given.　The　numerical　results　are　compared　with　those　of　the　theoretical　solution　and　the　assumed　displacement　finite　element　method　based　on　potential　energy　principle.　It　has　been　demonstrated　that　the　new　finite　element　formulations　proposed　in　this　paper　is　effective,　accurate,　and　capable　of　simulating　the　large　rotation　case　under　one　large　load　step.