  We introduce a new screening function which is useful for the few-body
Coulomb scattering problem in ``screening and renormalization'' scheme. The new
renormalization phase factor of the screening function is analytically shown.
The Yukawa type of the screening potential has been used in several decades, we
modify it to make more useful. As a concrete example, we compare the
proton-proton scattering phase shifts calculated from these potentials. The
numerical results document that high precision calculations of the
renormalization are performed by the new screening function.
