Droplets of Zr41 Ti14Cu12.5Ni10Be22.5 glass-forming alloy with different sizes are solidified in a drop tube containerless process. The glass transition temperature Tg of Zr41 Ti14 Cu12.5Ni10Be22.5 glassy spheres solidified with different cooling rates is investigated by using a differential scanning calorimeter. It was found that all the amorphous spheres show an increase of Tg with the heating rate. The glassy spheres have a unique value for the glass transition activation energy E9 = 435.50 k J/mol, which is independent of cooling rate q. The insensitivity of Tg to q is interpreted by an extension of the free volume model for flow.