In this paper, we study a modified Hegselmann - Krause model of opinion dynamics based on the bounded confidence principle.
This model is formulated as a discontinuous and nonlinear dynamical system. At any time moment of the process of opinion formation,
the operator of forming the next opinion of an agent is two-step; first, one takes the average of opinions of agents sharing similar opinions plus his/her own; in the second step, a regularization procedure is performed. A new regularization procedure is applied. We find conditions under which every trajectory tends to a fixed point of the system and study stability properties of fixed points.