A previously developed theory of the angular distribution and intensity of photoelectrons ejected from diatomic molecules is used to consider the potential information contained in rotational fine structure in molecular photoelectron spectroscopy. It is shown that resolution of such structure would permit the evaluation of contributions corresponding to the terms in a one-centre expansion of the molecular orbital from which the photoelectron is ejected. The case of H2is analysed in detail, and the analysis compared with that of Tully, Berry and Dalton.