It is shown that for a general asymmetric directional coupler formed by two electromagnetic transmission lines, resistive terminations can be chosen so that the normal modes of the coupled system are reflected without conversion from one to the other. With such ‘non-mode-converting’ terminations the scattering matrix assumes a particularly simple form which can readily be interpreted physically. Practical means of finding the value of non-mode-converting terminations are indicated and the behaviour of couplers with non-mode-converting terminations is predicted.