From the appearance of CodeRed and SQL Slammer worm, we have learned that the early detection of worm epidemics is important to reduce the damage caused by their outbreak. One prominent characteristic of Internet worms is to choose next targets randomly by using a random generator. In this paper, we propose a new worm detection mechanism by checking the random distribution of destination addresses. Our mechanism generates the traffic matrix and checks the value of rank of it to detect the spreading of Internet worms. From the fact that a random binary matrix holds a high value of rank, ADUR (Anomaly Detection Using Randomness check) is proposed for detecting unknown worms based on the rank of the traffic matrix. From the experiments on various environments, we show that the ADUR mechanism effectively detects the spread of new worms in an early stage, even when there is only one host infected in a monitoring network.