Abstract: In this paper, the calculation of the bilinear Boltzmann operator based on the Waldmann's method^[1] for Maxwellian molecules has been given. The advantage of our technique lies in the calculation need not operato on the integral of operator. The way of carrying out the calculation is illustrated by several examples containing all proofs of the formulas in the article by Chen Tianquan & others^[4]. Moreover, for the linear Boltzmann operator, the calculation is slightly simpler than that of Waldmann^[1].