It is proved that the S matrix element S(λ, k) for the z-4 repulsive potential → 1 as |λ|→∞ in the sector 0 ≤| argλ | <π 2-ε and that it has infinitely many reggepoles in a small angle neighbourhood of the imaginary axis with their real parts approaching ∞ simultaneously. ordinary double dispersion relation does not hold this case.< div>