We investigate whether the behavior of the pitch angle, predicted by a local dispersion relation derived from the density wave theory, can be applied to that of the fastest growing, globally unstable modes of flat stellar disks. We pay attention to two-armed modes, and obtain such global modes by numerically integrating the linearized collisionless Boltzmann equation. The results show that the pitch angle of the fastest growing modes has a tight correlation with the ratio of the square of the radial velocity dispersion to the surface density, as indicated by the local theory, over a sufficiently wide range of radii. The correspondence between the global modes and global properties of spiral galaxies is briefly discussed.