Dissociative adsorption of molecular hydrogen on clean Si(001) surfaces has been investigated by means of scanning tunneling microscopy. The dissociated hydrogen atoms are found to occupy Si atoms of adjacent dimers. In addition to this interdimer configuration associated with the adsorption of isolated hydrogen molecules, pairs of adjacent doubly occupied dimers are readily formed. They arise from the enhanced reactivity of partially occupied dimers following the initial H2 adsorption step. The results are considered in light of recent adsorption and desorption measurements.