Abstract: In this paper, the search capability of common crossover operator is discussed. By studying the dual function of the crossover operator, the rule of the amount and range of the chromosome are obtained. It was proved that the genes would be independent. It was also proved that the limit probability of the schemate equals the product of the initial probability of the genes and had nothing to do with the definition length of the schemate. By this study the performance of the genetic algorithm can be improved.