The transient stability analysis of power systems can be described by differential and algebraic equations, and due to the increased speed with parallel computing techniques, use of the waveform relaxation method to solve these equations has attracted much attention. In order to enhance the calculation speed of the waveform relaxation method, it is of prime importance to reduce the required number of iterations for each time window. To this end, an initialization and preconditioning techniques have been proposed to improve convergence of the iterative procedure. In this paper, in order to enhance convergence, we developed a new global initialization technique that consists of linear analysis and a preconditioning technique. Specifically, global initialization is the result of the repeated application of conventional initialization and preconditioning techniques before each of the nonlinear iterative procedures, and then using linear analysis to determine the interaction between the CPUs. By calculating the initial waveforms more accurately, it is expected that additional speedup can be achieved by reducing the required number of iterations necessary for convergence of the nonlinear analysis.