In a recent publication (Moggride, 2012a), a simple equation was shown to accurately predict the mutual diffusion coefficients for a wide range of non-ideal binary mixtures from the tracer diffusion coefficients and thermodynamic correction factor, on the physical basis that the dynamic concentration fluctuations in the liquid mixture result in a reduction of the mean thermodynamic correction factor relative to the hypothetical case in which such fluctuations do not occur. The analysis was extended to cases where strong molecular association was hypothesised to occur in the form of dimerization of a polar species in mixtures with a non-polar one. This required modification of the average molecular mobility in the form of doubling the tracer diffusivity of the dimerized species (Moggridge, 2012b). Predictions were found to show good accuracy for the mixtures investigated. One of the difficulties with this approach is that it is an a posteriori correction: there is no a priori way of knowing whether strong cluster formation influences the observed molecular mobility, or what the appropriate size of the cluster is. In this work, a modification is made to the average molecular mobility in the original equation by replacing the bulk mole fraction with local mole fraction calculated using the NRTL (non-random two liquid) model, to take account of strong molecular association that results in highly correlated movement during diffusion. The new equation enables an accurate description of mutual diffusion coefficients in mixtures of one strongly self-associating species and one non-polar species, as well as in non-ideal, non-associating mixtures. This result is significant because in this way there is no need of any prior knowledge on the degree of molecular association in the mixture for the prediction of mutual diffusion coefficients from tracer diffusivities.