Abstract: Numerical calculation of crossovers is important groundwork for satellite altimeter data processing. The criteria for judging the existence of crossover are extended to be applicable to any two satellite ground tracks. A fast numerical algorithm named rectangle shrinking method is proposed in order to improve the computational efficiency. Based on a cycle of simulated orbit data of Topex/Poseidon (T/P) and a pass of observations from HY-2, two experiments are performed to assess the precision and efficiency of the algorithm. The results demonstrate that the rectangle shrinking method can rapidly work out all of crossovers with high precision. Another test on Envisat data validated the applicability to near polarorbit. The proposed algorithm has strong universality, not only solving the crossovers from tracks of a single satellite, but also two satellites with different inclinations.