Rotation used to be thought as an effective method to prohibit the formation of freckles of a binary alloy unidirectionally solidified from below, which we will show in the present paper is true only under restrictive conditions. A linear stability analysis is implemented for the system consisting a dendritic mushy region underlying a bulk fluid region and relating uniformly about a vertical axis. Emphasis is placed on the rotation effects on the competition between the convection modes, which has a direct influence on the formation of freckles. Results show that rotation generally enhances the stability of the convection modes, but the enhancement is not significant until the rotation speed is very high (such as 10(5) rpm), which in some sense agrees well with the previous numerical and experimental results. in spite of its ineffectiveness as an inhibitory method to the formation of freckles, it is found from the present parametric study that the effects of rotation on convection depend largely on the buoyancy ratio A of the alloy. Both the changes of the rotation speed and the buoyancy ratio may lead to a switch of the most critical convection mode, which may in turn influence the characteristics of the subsequent plume convection, and thus the formation of freckles.