In the recent years it has been shown that behavior of the human social activities can be successfully simulated by quite simple models. Among them, very interesting due to its discrete representation, seems to be cellular automata. In the presented paper we would like to deal with this approach introducing some corrections to the model of cellular automata with two absorbing states. The simple version of this model has already been used in simulations of the opinion formation by Bagnoli and the obtained results were very promising. Our modifications lead to the new phase diagram shown in the paper. We present also general differences implicated by the Bagnoli's model modifications.