Abstract: In this paper, the notions and concepts about information set, semi-convergence, strong convergence, etc. are introduced and the definitions of transient efficient solution as well as its stationariness in multi-step decision process are given. Then the paper studies the relation between the conergence in the sense of topology and the strong convergence in the sense of pompeiu-Hausdauff Matrix, and proves the corresponding theorems trader weak conditions. Finally the paper systematically investigates the stationariness of efficient solution sequence.