A strong effect of radiation damping on the interaction of an ultraintense laser pulse with an overdense plasma slab is found and studied via a relativistic particle-in-cell simulation including ionization. Hot electrons generated by the irradiation of a laser pulse with a radiance of I lambda(2)>10(22) W microm(2)/cm(2) and duration of 20 fs can convert more than 35% of the laser energy to radiation. This incoherent x-ray emission lasts for only the pulse duration and can be intense. The radiation efficiency is shown to increase nonlinearly with laser intensity. Similar to cyclotron radiation, the radiation damping may restrain the maximal energy of relativistic electrons in ultraintense-laser-produced plasmas.