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In this paper, we extend our previous work of StablePlus, a stable scheduling algorithm for single-stage packet switches, to bufferless three-stage Clos-network switches. StablePlus is based on an existing stable distributed scheduling algorithm, called DISQUO. We further improve the switching performance by incorporating a heuristic scheduling algorithm after the DISQUO scheduling. In a three-stage Clos-network switch, DISQUO is first used to solve the output contention which generates a stable matching between the input and output ports, then Karol's algorithm is used to find the feasible internal paths for the matched input and output pairs. However, the latter requires multiple mini-cycles to complete the path-finding task. Worse is that the number of mini-cycles increases as the switch size does, limiting the Clos-network to a small implementable size. By replacing the Hamiltonian Walk in DISQUO with time-division multiplexing (TDM) scheme, we show that the number of required mini-cycles for Karol's algorithm can be reduced to only two, independent of the switch size. Moreover, with the help of a parallel hardware approach, we can implement packet scheduling in O(1) time complexity. To support high data rates, e.g., 100 Gbps, we can also make the scheduling work on a frame basis. We prove that StablePlus can achieve 100% throughput under any admissible traffic, and by simulations we show that it also has good delay performance.