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In recent years, multi-regional trials have received increasing attention by pharmaceutical companies carrying out global drug development programs. In Japan, new drugs are often approved several years after market release in other countries. The recently published guidance on 'Basic Principles on Global Clinical Trials' addresses specifically this time lag. A multi-regional trial has at least two main objectives. First, it is necessary to show a significant benefit in effect of a new drug in the entire population. Second, one needs to demonstrate that the results for a particular region are consistent with those from the entire population. In this paper, we discuss the methods proposed in the Japanese regulatory guidance document and derive closed form expressions for the resulting probabilities, which require the evaluation of multivariate normal or t probabilities. In addition, we propose an alternative method with better operating characteristics than the current approaches. Moreover, we examine the performance of our suggested method by simulating the probability of achieving the objectives and calculating the false-positive error rate.