Phase selection, a common and important phenomenon in rapid solidification, determines the solidification sequence and the mechanical/physical properties. In this work, a Co-20 at%B hypereutectic alloy was undercooled by the melt fluxing technique and the microstructure was characterized by the back-scattering diffraction technique. A transition from hypereutectic to hypoeutectic was found at a critical undercooling of Delta T = 119 K. When Delta T < 119 K, a primary directional dendritic beta-Co3B phase surrounded by the regular alpha-Co +beta-Co3B lamellar eutectics was found. When Delta T > 119 K, the above hypereutectic microstructure changes into hypoeutectic structure with the alpha-Co phase as the primary phase. According to dendrite growth model, the transition from hypereutectic to hypoeutectic can be ascribed to the higher growth velocity of the a-Co phase than the beta-Co3B phase, i.e., the growth-controlled mechanism. The current work shows also that there is a coupled zone skewed to the beta-Co3B phase in the Co-B alloys system.