A modified differential correction method is introduced to generate Lyapunov periodic orbits at collinear equilibrium points in the planar restricted three body problem. An intermediate step in which an update for initial velocity is obtained from the Jacobi integral equation is added to the correction process. The method can be used at higher amplitudes from the libration points where the regular correction method shows divergence especially when the third body approaches the second primary. The method is preferred when obtaining a periodic orbit in the neighborhood of an existing Lyapunov orbit and a family of orbits within a small range of energy level can be obtained.