The dual reciprocity method (DRM) has been successfully employed along with the boundary element method (BEM) to simulate non linear flow phenomena such as convective momentum transport and shear thinning fluids. In the latter however, domain partitioning has been necessary to achieve convergence when the power law index is below 0.8. This paper shows how a single domain DR-BEM formulation for non Newtonian low Reynolds number flows can be implemented in order to obtain accurate results for lower values of the power law index. Some of the characteristics of this implementation are the use of quadratic elements and an iterative solution of the non linear system of equations using a modified Newton-Raphson method. Along with the implementation, two radial basis functions (RBFs) were used and compared on two classical problems of inelastic non Newtonian flow: couette mixing and slit flow. Solutions obtained are also compared to results from a multi-domain dual reciprocity method (MD-DRM) for equal meshes. Results showed that using the above mentioned strategies, single domain DR-BEM can accurately predict the flow field in inelastic non Newtonian flow for values of the power law index as low as 0.5. It is also worth noting that the accuracy of the single domain strategy was shown to be higher than MD-DRM, although the latter clearly reduced computational resource consumption.