We include atomic disorder in correlated narrow-band systems by assuming that the atomic level position fluctuates according to the Lorentzian distribution. We use the  Lloyd exact form of the averaged single-particle Green function when the electronic correlations are absent or treated in the saddle-point slave-boson (or Gutzwiller) approximation. The weak disorder reduces drastically the threshold for the Mott--Hubbard localization.

PACS numbers: 71.27.+a, 71.30.+h, 71.23.--k