The one-dimensional Heisenberg model with S= 1/2 is treated with the use of the two time Green's functions. The hierarchy of the equations of motion of the Green's functions is decoupled at a stage one-step further than Tyablikov's decoupling. The thermal average of the spin component, <Sz), is set to zero, because the long-range order does not exist in one dimension. Instead, our Green's functions are expressed in terms of the correlation functions cn=4<S 0zSnz). The Green's function is essentially of the form representing undamped spin waves, whose spectrum depends on ct, c2 and one more parameter. They are determined by the requirement that c 1 and c2 should be self-consistent and that co should be unity. The self-consistency equations have been solved analytically at high- and low-temperature limits, and also solved numel:ically in the whole range of the temperature. Thermodynamic quantities have been calculated using these ·solutions. It has turned out that the theory gives the correct high-temperature expansion for the thermodynamic quantities and the correlation functions. The latter is expressed by en= (Jj4kBT)n. In the case of ferromagnetic coupling, the correlation function en at T=O is equal to 1/3 for all n's. This is what is expected from the correct ground state of the ferromagnetic Heisenberg system. The spin-wave spectrum at T=O also agrees with the correct one. At T4:;JfkB, we find that the specific heat goes as T 112 and the suscepti bility goes as T-2• The gross feature of the temperature-dependence of the thermodynamic quantities agrees with Bonner and Fisher. In the case of the antiferromagnetic Heisenberg model, we find cl=-0.55407 and c2=0.16100 at T=O, which are fairly close to the exact values. The thermodynamic quantities are also in gross agreement with Bonner and Fisher.