A thread-tapping screw (11) has a thread (21) extending, starting from the screw shaft free end (15), at least along a portion of the shaft length and a height of which constantly decreasing toward the free end (15) of the shaft (12), and a plurality of cutting bodies (26, 36, 46, 56, 66) formed of a material having a greater hardness than hardness of the thread (21), located in recesses (24) formed in the thread (21) and opening radially outwardly and having, respectively, a radial outer profile (27, 37, 47, 57, 67) projecting, at least partially, beyond the thread and a height (A, B, C, D, E) of which decreases toward the free end (15) of the shaft (12) stepwise.