This paper proposes a Bartlett–corrected Lagrange multiplier statistic for the test of het-eroskedasticity. Under the null hypothesis, the test based on this improved statistic and the test based on modified critical values are equivalent to order n^–1, where n is the sample size. We also give matrix expressions for the coefficients used in the corrections and a small program written in the S–PLUS language for the computation of such coefficients. Closedform expressions for the corrections in some simple models are also derived. Simulation results show that both corrected tests have empirical sizes closer to the nominal size than the original Lagrange multiplier test of heteroskedasticity.