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Eliciting and describing complex business process consistently and unambiguously is important and critical for migrating complex business processes to cloud platform. Mspoa (Subject Predicate Object Adverbial complex business process description Meta-model) is proposed in this paper, which can represent the static relationship in business process description problem space. Based on Mspoa, clewed and cored by form business process, CBPM (Complex Business Process Model) is presented to describe dynamic behavior relationship. By the means of the migration steps described in this paper, incoherence and bounce in the course of business processes analysis can be overcome, assuring the correctness of the artifacts.