Summary: In this study, we present a multivariate test for population bioequivalence. Recently, I. Chervoneva et al. [“A multivariate test for population bioequivalence”, Stat. Med. 26, No. 6, 1208–1223 (2007; doi:10.1002/sim.2605)] proposed a multivariate generalization of the criteria for testing univariate population bioequivalence by obtaining an approximate test based on an unbiased estimator of linearized criteria. Their test involved decomposing the unbiased estimator into several terms and using the existing interval estimates of these terms. Although this test’s type I error probability is often lower than the nominal significance level, its approximation accuracy is not good in case of small samples. This study intends to present a more accurate approximate test. To improve the accuracy, it is important to investigate the distribution of the unbiased estimator of the linearized bioequivalence criteria. Therefore, we derive an explicit representation of its characteristic function and asymptotic distribution and propose new tests that exploit the asymptotic results. We additionally obtain the theoretical asymptotic power function in an explicit manner and investigate the local powers of our test, proving that they are asymptotically unbiased. Further, we investigate their finite-sample performance via Monte Carlo simulations and confirm that the accuracy is better as compared to that observed in a previous test. Finally, we use our methods to analyze real data.