Experimental investigations [1] show that when allowance is made for the real properties of a gas it is possible to have a regime of regular reflection of a shock wave from the surface of a wedge in which the reflected shock wave is attached to the tip of the wedge. In the present paper, which uses perturbation theory in a form close to a modified small-parameter method [2], an approximate analytic solution is constructed to the problem of the interaction of a strong shock wave with the surface of a wedge for such a regime. In contrast to the problem considered by the same authors in an earlier paper [3], the half-angle at the tip of the wedge is not assumed to be small.