The strain-accommodating mechanism of formation of the saw-tooth microstructure in the L12+L10 two-phase ordered system is proposed. To describe the atomic scale kinetics of ordering and decomposition in this system, the master equation, which explicitly incorporates the effect of the transformation strain, is formulated. It is used to simulate the precipitation of the L10 phase from the L12 parent phase in the Co±Pt alloy. The computer simulation shows that the decomposition occurs heterogeneously on antiphase boundaries of the L12 structure if the composition is near the solubility limit of the L12 phase. It eventually produces the saw-tooth microstructure. The decomposition transforms the (010) anti- phase boundary into a layer of the single-variant tetragonal L10 phase separating the L12 antiphase domains. Later, the strain accommodation transforms this single-variant L10 phase layer into the saw- tooth pattern. The simulation results are in excellent qualitative and quantitative agreement with our TEM images of Co38.5Pt61.5.