For a completely integrable nonlinear equation, the Poisson bracket of monodramy matrix is known to be expressed in a form of integral with respect to x. The integrand is found to be an x-differential of a linear combination of direct product of two pairs of Jost solutions definitely, and the coefficients can be determined by comparing the corresponding elements of direct product matrices on two sides. Hence a general procedure for constructing Hamiltonian formalism is given for a completely integrable nonlinear equation. As an example, the Hamiltonian theory of sine-Gordon equation is re-exam...
