The paper introduces a new method for solving the problem of calculating the perturbed trajectory of a two-impulse flight between a near-lunar orbit and a halo orbit in the vicinity of the L2 point of the Sun — Earth system. Unlike traditional numerical methods, this method has better convergence. Accelerations from the gravitational forces of the Earth, the Moon and the Sun as point masses and acceleration from the second zonal harmonic of the geopotential are taken into account at all sections of the trajectory. The calculation of the flight path is reduced to solving a two-point boundary value problem for a system of ordinary differential equations. The developed method is based on the parameter continuation method and does not require the choice of an initial approximation for solving the boundary value problem. The last section of the paper provides examples and results of the analysis based on this method.