Suppose we have to choose two objects from a finite set which consists of $N$ objects. Let the set be ordered by quality. Let us enumerate the objects in the order in which we observe them. After observing $a_s$ we know comparative qualities of $a_1,a_2,\dots,a_s$ but we know nothing about the quality of the remaining $N-s$ objects. While observing $a_s$ we can accept it (thus making the first choice) or reject it (then it will be impossible to return to it). We find an optimal policy which provides the greatest probability of choosing two best objects and describe its asymptotical behaviour as $N\to\infty$ .