The Balloon-borne Experiment with a Superconducting Spectrometer (BESS) has carried out precise observation of the low-energy cosmic rays. Using a tracking system (in a 0.8 T uniform magnetic field) with a rigidity resolution of ∼0.4% at 1GV and a time-of-flight system with a time resolution of 120 ps, the BESS instrument enables us to distinguish isotope events. In December-January 2007-2008, BESS-Polar II achieved a 24.5-day observation during its balloon flight over Antarctica. By using 4.7 billion cosmic-ray event data obtained during the flight, rare $^{10}$Be events have been searched and analyzed. In this paper, we will report the analysis process of the beryllium isotope ratio measured by the BESS-Polar II.