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A fast algorithm is proposed to find the nondominated set for multiobjective optimization problems in this paper. Two accelerated techniques are adopted in the algorithm. One is that the algorithm can yield an integer rank set after it indexes the search space. Based on this, the goal is changed into determination of the nondominated set of the integer rank set. The other is that the nondominated check sequence follows that the likely nondominated members are first checked, and that the check process is stopped when the remaining members in the nondominated check sequence are dominated. The computational complexity of the new algorithm is analyzed theoretically. Experimental results show that the new method performs much better than KLP (a famous effective algorithm) when the search space contains a large nondominated set. Moreover, the two new techniques introduced in this paper are very useful for multiobjective evolutionary algorithms (MOEAs) to improve the computational speed.