Thermal-gravitational instability (TGI) is studied in the protogalactic environment. We extend our previous work, in which we found that dense clumps first form out of hot background gas by thermal instability and that later a small fraction of them grow to virialized clouds of mass M-c greater than or similar to 6 x 10(6) M-. by gravitational infall and merging. But these clouds have large angular momentum, and so they would have difficulty ( although it would not be impossible) further evolving into globular clusters. In this Letter, through three-dimensional hydrodynamic simulations in a uniformly rotating frame, we explore whether or not the Coriolis force due to rotation in protogalactic disk regions can hinder binary merging and thus reduce the angular momentum of the clouds formed. With rotation comparable to the Galactic rotation at the solar circle, the Coriolis force is smaller than the pressure force during the early thermal instability stage. So the properties of the clumps formed by thermal instability are not affected noticeably by rotation, except for increased angular momentum. However, during the later stage, the Coriolis force becomes dominant over the gravity, and hence the further growth of gravitationally bound clouds by gravitational infall and merging is prohibited. Our results show that the Coriolis force effectively destroys the picture of cloud formation via TGI, rather than alleviating the problem of large angular momentum