The so-called star-forming main sequence of galaxies is the apparent tight relationship between the star formation rate and stellar mass of a galaxy. Many studies exclude galaxies which are not strictly ‘star forming’ from the main sequence, because they do not lie on the same tight relation. Using local galaxies in the Sloan Digital Sky Survey, we have classified galaxies according to their emission line ratios, and studied their location on the star formation rate–stellar mass plane. We find that galaxies form a sequence from the ‘blue cloud’ galaxies which are actively forming stars, through a combination of composite, Seyfert, and low-ionization nuclear emission-line region galaxies, ending as ‘red-and-dead’ galaxies. The sequence supports an evolutionary pathway for galaxies in which star formation quenching by active galactic nuclei plays a key role.