There are a number of data dependence tests that have been proposed in the literature. In each test there is a different trade-off between accuracy and efficiency. The most widely used approximate data dependence tests are the Banerjee inequality and the GCD test; whereas the Omega test is a well-known exact data dependence test. In this paper we present a new, fast data dependence test for array references with linear subscripts, which is used in a vectorizing compiler for microprocessors with a multimedia extension. Our test is suitable for use in a dependence analyser that is organized is as a series of tests, progressively increasing in accuracy, as a replacement for the GCD or Banerjee tests.