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Abstract: The tripartite entanglement is examined when one of the three parties moves with a uniform acceleration with respect to other parties. As Unruh effect indicates, the tripartite entanglement exhibits a decreasing behavior with increasing the acceleration. Unlike the bipartite entanglement, however, the tripartite entanglement does not completely vanish in the infinite acceleration limit. If the three parties, for example, share the Greenberger-Horne-Zeilinger or W-state initially, the corresponding $π$-tangle, one of the measures for tripartite entanglement, is shown to be $π/6 \sim 0.524$ or 0.176 in this limit, respectively. This fact indicates that the tripartite quantum information processing may be possible even if one of the parties approaches to the Rindler horizon. The physical implications of this striking result are discussed in the context of black hole physics.