In a cooled blade for a gas turbine, a cooling fluid, preferably cooling air, flows for convective cooling through internal cooling passages located close to the wall and is subsequently deflected for external film cooling through film-cooling holes onto the blade surface. The fluid flow is directed in at least some of the internal cooling passages in counterflow to the hot-gas flow flowing around the blade. Homogeneous cooling in the radial direction is achieved by providing a plurality of internal cooling passages and film-cooling holes arranged one above the other in the radial direction in the blade in such a way that the discharge openings of the film-cooling holes in each case lie so as to be offset from the internal cooling passages, and in particular the discharge openings lie between the internal cooling passages.