Global existence of small amplitude solution and nonlinear scattering result for the Cauchy problem of the generalized IMBq equation were considered in the paper titled Small amplitude solutions of the generalized IMBq equation [1]. It is a pity that the authors overlooked the bad behavior of low frequency part of S(t)ψ which causes troubles in L∞ and Hs estimates. In this note, we will present a new proof of global existence under same conditions as in [1] but for space dimension n ≥ 3.