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For the first time, the problem of scheduling divisible loads in a single-level tree network in the non-blocking mode of communication is considered. All earlier studies in divisible load scheduling have considered the blocking mode of communication. A closed-form expression for the processing time in non-blocking mode of communication is derived. Using this closed-form expression, this paper analytically proves a number of significant results on load sequencing and processor-link arrangement in a single-level tree network.