The time-displacement operator for Hamiltonian dynamical systems M(t|t₀) is a symplectic transformation - Lie map. Any truncated Lie map (Lie approximant) loses the very important symplectic property. In this report a method of correcting the truncated map is given. The matrix representation for desired symplectic map is calculated in the symbolic form. The symplectification conditions have the form of simple linear algebraic equations. The symbolic solutions of these equations are computed in advance and are stored in a database. This approach allows us to simplify the calculation process for the evolution of dynamical systems, in particular, for long time evolution.