The infrared divergence of the interaction among Bogoliubov's quasi-particles in a degenerate boson system can be avoided by introducing improved quasi-particles. A formula is given which relates the single-particle operators aP directly to the improved quasi-particle operators bP, which have been defined in terms of collective, variables in a preceding paper. The operators aP are expressed in terms of bP as a series using N-1/2 as a formal expansion parameter, where N is the number of particles in the system. Terms up to order N-3/2 are given together with a term of order N-2 which is necessary for the calculation of the ground-state energy to order N-2. The formula makes the reason clear why the operators bP enable us to eliminate the ultraviolet divergence haunting collective theories including the quantum hydrodynamics.