It is revealed by in situ transmission electron microscopy that a unique, fluid amorphous phase is produced in Sn-Bi alloy particles at room temperature when the size of particles is below 10 nm. Bright and dark spots in the granular contrast in the high-resolution electron microscopy images of the fluid amorphous phase exhibited continuous changes in position and intensity with time, suggesting a high atomic mobility in the amorphous phase. Upon heating the fluid amorphous phase went to melt without crystallization and upon cooling it solidified again into the fluid amorphous phase with no traces of crystallization. These results indicate that due to the finite-size effect, the eutectic point T-eu in this system is lowered to a temperature below room temperature where observations were carried out, and that the glass transition temperature T-g, where a liquid goes to an amorphous solid, locates near room temperature.