This paper proposes a new multistart algorithm to find the global minimum of constrained problems. This algorithm, which in this paper is called the repulsion algorithm, efficiently selects initial design points for local searches. A Bayesian approach provides the stopping rules. The method uses information from the previous sampling points and the corresponding sequences generated by local searches to select new initial points. This approach increases the probability of finding all local minima with fewer local searches. Numerical example problems show that compared with traditional multistart methods, the repulsion algorithm reduces significantly the number of local searches required to find the global minimum.