An Adaptive Random Testing(ART) is one of test case generation algorithms, which was designed to get better performance in terms of fault-detection capability than that of Random Testing(RT) algorithm by locating test cases in evenly spreaded area. Two ART algorithms, such as Distance-based ART(D-ART) and Restricted Random Testing(RRT), had been indicated that they have significant drawbacks in computations, i.e., consuming quadratic order of runtime. To reduce the amount of computations of D-ART and RRT, iterative partitioning of input domain strategy was proposed. They achieved, to some extent, the moderate computation cost with relatively high performance of fault detection. Those algorithms, however, have yet the patterns of non-uniform distribution in test cases, which obstructs the scalability. In this paper we analyze the distribution of test cases in an iterative partitioning strategy, and propose a new method of input domain enlargement which makes the test cases get much evenly distributed. The simulation results show that the proposed one has about 3 percent of improvement in terms of mean relative F-measure for 2-dimension input domain, and shows 10 percent improvement for 3-dimension space.