In this paper, we study the limit behavior of trajectories of a nonlinear and discontinuous model of opinion dynamics based on the notion of bounded confidence. This model was previously studied in the case where the influence function has the form i(v) = v. It was shown that, under a particular condition on parameters of the system, any its trajectory tends to a fixed point. In this paper, we prove a similar result under weaker conditions on the influence function: it is assumed that i(v) is continuous, nonstrictly increasing, and i(v) = 0 if and only if v = 0.