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The throughput of multi-hop communication systems can significantly be increased by the application of MIMO concepts. To utilize the physical resources in an efficient way while meeting the quality-of-service (QoS) constraints, appropriate power allocation strategies are desired. In this paper the total transmit power of a MIMO multi-hop system is minimized under the constraint of a given end-to-end outage probability. The optimum power allocation corresponds to a convex optimization problem. In order to achieve an analytical solution, the original task is relaxed by stringent approximations and a simple closed- form near-optimum solution is proposed. As this improved approximative power allocation (IAPA) achieves excellent performance results, this new approach is also very useful for investigating outage restricted multi-hop systems analytically.