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The importance of anharmonic effect in dissociation of molecular systems especially clusters has been noted.In this paper, we shall study the effect of coupled anharmonic oscillator of the standard bilinear form (SBF) Morse oscillator (MO) potential and simple oscillator on unimolecular reaction.We shall use the systematic theoretical approach (YL method), proposed by Yao and Lin [Yao, L., et.al.J.Phys.Chem.A, 2007, 111 (29), 6722-6729], which can evaluate anharmonic effects on the rate constants within the transition state theory.