Low-energy electron microscopy (LEEM) was used to investigate Si homoepitaxial growth on Si(111)√3×√3-B. Dark-field LEEM images using the (1,0) spot clearly indicate that two-dimensional islands twinned with respect to the substrate nucleate in the initial growth stage. Coalescence of the twinned islands forms twinned epitaxial layers at low growth temperatures. At high temperatures, however, twinned islands are transformed into untwinned islands even during growth, which suggests that small islands favor the twinned orientation, but that the energy difference between twinned and untwinned islands is reversed at a certain island size. After twinned epitaxial layer growth, we also observed transformation into untwinned layers by annealing. The transformation proceeds through the motion of the boundary between twinned and untwinned layers along the surface.