An efficient and precise data dependence analysis is the key to the success of a parallelizing compiler because it is required in almost all phases of the parallelism detection and enhancement in such compilers. However, existing test algorithms are quite weak in analyzing multi-dimensional array references, which are usually where the parallelism is in most programs. In this paper, a new algorithm, called X-test, is presented for an efficient and accurate data dependence analysis on multi-dimensional array references. It achieves high efficiency and high accuracy at the same time, which is in general not allowed in previous algorithms. This algorithm has been implemented in Parafrase [Wolf82]. Some experimental results are also presented to show its effectiveness.