A series of numerical experiments on the two-dimensional decaying turbulence is performed for a non-divergent barotropic fluid on a rotating sphere by using a high-resolution spectral model. Time variations of the energy spectrum and the flow field are highly dependent on the rotation rate. In non-rotational cases, isolated coherent vortices emerge in the course of time development as in the planar two-dimensional turbulence. As the rotation rate increases, however, the evolution of the flow field changes drastically, and a westward circumpolar vortex appears in high-latitudes as well as zonal band structures in mid- and low-latitudes. Dependence of these features on the initial energy spectrum is investigated and the dynamics of such pattern formations is discussed.