We use the recent releases of sensitive VLA/LOFAR large-area surveys at 340 MHz and 54 MHz, in conjunction with the 1.4 GHz NVSS, to accurately determine the `spectral index-flux density relation' (α − S) for extragalactic radio sources selected at metre and decametre wavelengths, with the latter explored for the first time. This newly determined α − S340 MHz relation shows a progressive flattening of αmedian towards lower flux densities, starting from its steepest value (peak) occurring near S340 MHz ∼ 1 − 2 Jy. This resolves the controversy extant in the literature since the 1980s. The α − S54 MHz relation also shows a spectral index flattening with decreasing flux density which is, however, significantly milder and the relation less sharply peaked than that found at 340 MHz. A possible reason for the difference could be that the 54 MHz sample has a distinctly stronger and more conspicuous presence ( at ∼20% level) of very steep spectrum sources having α541400 < −1.3, most of which are probably associated with clusters of galaxies.