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Recently, geometric routing has emerged as an efficient routing strategy on wireless networks. An ideal geometric routing is memoryless and does not suffer from the drawbacks of traditional proactive/reactive routings. All existing geometric routings on 3-D wireless networks either work deterministically only on the networks with special properties or do not guarantee delivery. In this paper, we divide the memoryless requirement into two sub-requirements, node-memoryless-ness and message-memoryless-ness. Then, we propose a new node-memoryless geometric routing, which is still free from the drawbacks of traditional routings. Our algorithm partitions the 3-D space with regular cubes and converts the routing problem over nodes into a routing problem over cubes. With minimal information attached to the header of a message, our algorithm deterministically delivers a message to its destination in any connected 3-D wireless networks. The forwarding decision on the message is made in a completely localized manner. The simulation results indicate that our algorithm outperforms its competitors on average.