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Using the strong coupling diagram technique a self-consistent equation forthe electron Green's function is derived for the repulsive Hubbard model. Termsof two lowest orders of the ratio of the bandwidth $\Delta$ to the Hubbardrepulsion $U$ are taken into account in the irreducible part of the Larkinequation. The obtained equation is shown to retain causality and gives thecorrect result in the limit $U\rightarrow 0$. Calculations were performed forthe semi-elliptical initial band. It is shown that the approximation describesthe Mott transition, which occurs at $U_c=\sqrt{3}\Delta/2$. This valuecoincides with that obtained in the Hubbard-III approximation. At smalldeviations from half-filling the density of states shifts along the frequencyaxis without perceptible changes in its shape. For larger deviations thedensity of states is modified: it is redistributed in favor of the subband, inwhich the Fermi level is located, and for $U>U_c$ the Mott gap disappears.

The Mott transition in the strong coupling perturbation theory