The dispersion relation of the nonlinear anti-symmetric surface mode (in the whole electromagnetic region of its existence) in a plasma slab bounded by a linear dielectric is derived for strong striction nonlinearity. The phase velocity is expressed in terms of the wave electric field amplitudes at the boundary and at the axis of the slab. Using the same method, the authors obtain the linear dispersion relation of the wave in a new form. The approximation of a weak nonlinearity is also mentioned.