Among algorithms that are used to solve the equations of motion, the symplectic integrator (SI) has the advantage of conserving the phase space-volume and ensuring a stable simulation. However, incorporating the explicit formula of the SI in a molecular simulation is feasible only for the systems whose Hamiltonian is described by K(p) + V(q), where the kinetic energy K and the potential energy V depend only on momenta p and coordinates q, respectively. Due to this limitation, explicit SI integrators cannot directly be applied to the Nose-Hoover equations of motion for the constant temperature molecular dynamics (MD) simulation. In this article, by applying the formula of the decomposition of the exponential Liouville operator to the Nose-Hoover equations, we have obtained a series of integrators for the constant temperature simulation which have the correct form of the Jacobian of the Nose-Hoover equations. The systems examined here are liquid water and a protein in water. From the results of the constant temperature simulations, where several variations of the integrators were employed, we show that a combination of the Suzuki＇s second order formula and the fourth order symplectic integrator of Calvo and Sanz-Serna generates a trajectory of much higher accuracy than the nonsymplectic Gear-predictor-corrector method for a given amount of CPU time.