Random Testing (RT) is a simple but widely used software testing method. Recently, an approach namely Adaptive Random Testing (ART) was proposed to enhance the fault-detection effectiveness of RT. The basic principle of ART is to enforce random test cases as evenly spread over the input domain as possible. A variety of ART methods have been proposed, and some research has been conducted to compare them. It was found that some ART methods have a preference of selecting test cases from edges of the input domain over from the centre. As a result, these methods may not perform very well under some situations. In this paper, we propose an approach to alleviating the edge preference. We also conducted some simulations and the results confirm that our new approach can improve the effectiveness of these ART methods.