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Based on network circulation formulation, the existence of feasible beam-to-beam switching modes for a satellite-switched time-division multiple access system is completely and transparently proved, where simultaneous transmissions on several carriers in each spot-beam are configured. Showing the linear independence of all but one augmented switching modes, a new bound of mn+2 is obtained on the number of switching modes, where m and n are the number of up-link and down-link beams, respectively. The time complexity for finding the whole sequence of switching modes and for finding the initial switching mode are improved to O(m2n2) and O(min(√K,(m+n)23/)mn), respectively. Practical implementation considerations are discussed.