Recently　the　extended　projection　neural　network　was　proposed　to　solve　constrained　monotone　variational　inequality　problems　and　a　class　of　constrained　nonmonotontic　variational　inequality　problems.　Its　exponential　convergence　was　developed　under　the　positive　definiteness　condition　of　the　Jacobian　matrix　of　the　nonlinear　mapping.　This　note　proposes　new　results　on　the　exponential　convergence　of　the　output　trajectory　of　the　extended　projection　neural　network　under　the　weak　conditions　that　the　Jacobian　matrix　of　the　nonlinear　mapping　may　be　positive　semidefinite　or　not.　Therefore,　new　results　further　demonstrate　that　the　extended　projection　neural　network　has　a　fast　convergence　rate　when　solving　a　class　of　constrained　monotone　variational　inequality　problems　and　nonmonotonic　variational　inequality　problems.　Illustrative　examples　show　the　significance　of　the　obtained　results.