The problem of Computer Science students' cheating in their homework assignments so far has been handled mainly through administrative punishment of the cheaters. The success of such an approach depends to a large degree on the ability of the instructor to recognize the fact of cheating, which is a complicated task. With a large number of students taking the course, identifying the cheaters sometimes requires considerable time. The author of this paper suggests a method of solving the cheating problem by changing the course grading policy. The suggested approach emphasizes the importance of regular checking of students' understanding the course material.