This　paper　revisits　the　planar　periodic　motions　around　libration　points　in　circular　restricted　three-body　problem　based　on　invariant　manifold　technique.　The　invariant　manifold　technique　is　applied　to　construct　the　nonlinear　polynomial　relations　between　xi-direction　and　eta-direction　of　a　small　celestial　body　during　its　periodic　motion.　Such　direct　nonlinear　relations　reduce　the　dimension　of　the　dynamical　system　and　facilitate　convenient　approximate　analytical　solutions.　The　nonlinear　directional　relations　also　provide　terminal　constraints　for　computing　periodic　motions.　The　method　to　construst　periodic　orbits　proposed　in　this　study　presents　a　new　point　of　view　to　explore　the　orbital　dynamics.　As　an　application　in　numerical　simulations,　nonlinear　relations　are　adopted　as　topological　terminal　constraints　to　construct　the　periodic　orbits　with　differential　correction　procedure.　Numerical　examples　verify　the　validity　of　the　proposed　method　for　both　collinear　and　triangular　libration　cases.