The fragmentation process of primordial-gas cores during prestellar collapse is studied using three-dimensional nested-grid hydrodynamics. Starting from the initial central number density of n sim10^3 cm^-3, we follow the evolution of rotating spherical cores up to the stellar density n simeq 10^{22} cm^-3. An initial condition of the cores is specified by three parameters: the ratios of the rotation and thermal energies to the gravitational energy (beta_0, and alpha_0, respectively), and the amplitude of the bar-mode density perturbation (A_phi). Cores with rotation beta_0 > 10^{-6} are found to fragment during the collapse. The fragmentation condition hardly depends on either the initial thermal energy alpha_0 or amplitude of bar-mode perturbation A_phi. Since the critical rotation parameter for fragmentation is lower than that expected in the first star formation, binaries or multiples are also common for the first stars.
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