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We performed $42$ simulations of the first star formation with initialsupersonic gas flows relative to the dark matter at the cosmic recombinationera. Increasing the initial streaming velocities led to delayed halo formationand increased halo mass, enhancing the mass of the gravitationally shrinkinggas cloud. For more massive gas clouds, the rate of temperature drop duringcontraction, in other words, the structure asymmetry, becomes more significant.When the maximum and minimum gas temperature ratios before and aftercontraction exceed about ten, the asymmetric structure of the gas cloudprevails, inducing fragmentation into multiple dense gas clouds. We continuedour simulations until $10^5$ years after the first dense core formation toexamine the final fate of the massive star-forming gas cloud. Among the $42$models studied, we find the simultaneous formation of up to four dense gasclouds, with a total mass of about $2254\,M_\odot$. While the gas mass in thehost halo increases with increasing the initial streaming velocity, the mass ofthe dense cores does not change significantly. The star formation efficiencydecreases by more than one order of magnitude from $\epsilon_{\rm III} \sim10^{-2}$ to $10^{-4}$ when the initial streaming velocity, normalised by theroot mean square value, increases from 0 to 3.

Formation of first star clusters under the supersonic gas flow -- I. Morphology of the massive metal-free gas cloud