Abstract： For the highly singular potential satisfying the conditions of ref. (Ⅰ), it is proved that the partial wave S-matrix element posseses the asymptotic behaviour S(λ,k)～Ce-nImλ as the imaginary values of angular momentum tending to infinity. From this we obtained the following conclusions:(1) The WATSON-SOMMERFELD transformation of the scattering amplitude does not hold.(2) Using the result of ref. (I) and above equation, we get existance of REGGE poles with real part tending to infinity in the little angle neighbourhood of the imaginary axis.