The asymmetric rib waveguide directional coupler has previously been considered a complex structure to analyse, because the symmetry relied on by large-scale numerical techniques has been destroyed. Asymmetric couplers, however, have many applications in optoelectronics and are thus important structures to model. Here, the recently developed spectral index method is successfully applied to the asymmetric coupler. The propagation constants corresponding to the two polarised lowest-order supermodes of the entire structure are determined numerically from a transcendental equation.