We study the effect of a single excluded site on the diffusion of a particle undergoing a random walk in a d-dimensional lattice. The determination of the characteristic function allows us to find explicitly the asymptotical behaviour of physical quantities such as the particle average position (drift) x (t) and the mean square deviation x 2 (t) − x 2 (t). In contrast to the one-dimensional case, where x (t) diverges at infinite times ( x (t) ∼ t 1/2 ) and where the diffusion constant D is changed due to the impurity, the effects of the latter are shown to be much less important in higher dimensions: for d 2, x (t) is simply shifted by a constant and the diffusion constant remains unaltered although dynamical corrections (logarithmic for d = 2) still occur. Finally, the continuum space version of the model is analysed; it is shown that d = 1 is the lower dimensionality above which all the effects of the forbidden site are irrelevant.