This paper deals with the non- linear stability of triangular libration points by numerical method. By forming Lagrangian about the triangular librationpoints and taking only second order terms in Lagrangian about triangular libration point the characteristic equations were established by Lagrangian equations of motion. Then by the nature of characteristic roots we found that the triangular libration points are also unstable.

Keywords: Restricted Three-Body Problem, Jean’s law, Space-Time-Transformation, Libration Points, Non-Linear Stability.