An analytic method has been applied to a biochemical pathway with coupling. The harmonic balancing technique can be used to determine the effects of coupling on the Goodwin metabolic pathway. Its behaviour is modelled by a set of coupled ordinary nonlinear differential equations. This one is transformed to a single feedback loop control with a nonlinear function and a linear filter. It is shown that coupling modifies the linear filter such that the frequency and the amplitude of the oscillations decrease. The results obtained here are derived by both analytical and numerical studies, and compared with previous stability analysis of associated pathways.