Based on the intuition that widely spread test cases should have greater chance of hitting the non-point failure-causing regions, several Adaptive Random Testing (ART) methods have recently been proposed to improve traditional Random Testing (RT). However, most of the ART methods require additional distance computations to ensure an even spread of test cases. In this paper, we introduce the concept of localization that can be integrated with some ART methods to reduce the distance computation overheads. By localization, test cases would be selected from part of the input domain instead of the whole input domain, and distance computation would be done for some instead of all previous test cases. Our empirical results show that the fault detecting capability of our method is comparable to those of other ART methods.