One of the basic mathematical models of plasma is the set of master equations for the distribution functions of ions and electrons with the Coulomb collision operators [1]. The master equation is written in the sixdimensional phase space uniting the coordinate space and velocity space. This model in the general form is intricate, because it is multidimensional and involves effects with substantially different characteristic times. However, particular cases allow a change from Cartesian coordinates (X, Y, Z, v1, v2, v3) to specially chosen phase variables separated into slow and fast variables. Then, averaging with respect to fast variables can be performed. This procedure reduces the dimension of the problem, excludes fast oscillating processes, and separates slow-evolution variations of the distribution function, which are of principal interest. We deal with a high-temperature toroidal plasma used in experiments on controlled thermonuclear fusion in tokamaks. In these systems, the degrees of freedom can be separated into three fast and three slow variables, and one can use the symmetry in the azimuth angle. After averaging with respect to the fast motions, the master equation with three phase variables is obtained. Various modifications of the averaging method for master equations were analyzed in many works. Their results were generalized and developed in [2]. However, the fundamental properties of the averaged Coulomb collision operator were not appropriately studied. In the initial master equation, the Coulomb collision operator (see, e.g., [3]) (i) vanishes for Maxwell distributions of particles with the same temperature and average transport velocity, (ii) conserves the number of particles, (iii) conserves the total momentum of particles, (iv) conserves the total energy of particles, (v) does not increase the H function (analog of the Boltzmann H theorem), and (vi) is elliptic. These are the six fundamental properties of this operator.