In this study, numerical method for a global stability analysis based on a linear perturbation equation and an approximate eigensystem analysis is introduced by an improvement of Chiba’s method, which is a numerical method for a global stability analysis. The advantage of the improved method is that we can reduce the computational procedure approximately half with increasing the accuracy of velocity disturbances of the global stability analysis. In order to examine the validity of the modified method, the onset of the oscillation in the flow around a two-dimensional cylinder is calculated. The mode of the transition from steady flow to oscillatory flow calculated by the improved method is consistent with the mode calculated by Chiba’s method. The influence of the size of the computational domain on the result of the global stability analysis is checked by calculating the stability of the flow in a certain region of the flowfield. At a supercritical condition, two types of the basic flows, symmetric-type and averaged-type, are used to calculate the stability of the flowfield. The result of the symmetric-type basic flow agrees with Zebib’s result whose basic flow is given by the symmetric flow. The averaged-type basic flow is obtained by averaging the CFD result of the oscillating flowfield at a supercritical condition. The frequency of the flow oscillation which is observed in the CFD result agree with not the result of symmetric-type but the result of the averaged-type basic flow.