A two-step agent-based mathematical model of negative rumor spread in the context of conflicting groups is presented. The GBN-Dialogue model builds on rumor theory, focuses on person-to-person interaction characteristics,and is dynamical. The model first estimates the probability of rumor transmission between two persons based on their transmission motivation (which is a function of their Group (G) memberships), the strengths of their belief (B) in the rumor, and the Novelty (N) of the rumor for each person. Psychological and sociological research informs this Transmission Probability Function. In the second step, belief levels and rumor novelty of each participant change as a result of rumor transmission and time; literature on attitude change guides these updating functions. Empirical support is presented by comparing rumor transmission literature with results of Monte Carlo simulations on different network topologies. The validity of the model's assumptions is addressed by comparison with simpler and more complex alternatives.