In this paper, we consider the propagation problem of multiple competing opinions over a network with antagonistic interactions, modeled as a signed graph. The sign attached to an edge in this graph characterizes the cooperative (positive edge) or antagonistic (negative edge) relation between agents. The agent randomly selects itself or one of its neighbors to determine its opinion. If the agent selects itself, it will stick to its own opinion; if the agent selects the neighbor that interacts with it in the cooperative way, it will adopt the neighbor's opinion. However, for the antagonistic interaction, the agent chooses one opinion from the competing opinions, subtracting its neighbor's opinion in nonuniform and uniform probability, respectively. According to the update rules established earlier, two propagation models are provided. For the nonuniform scenario, a new network is constructed and its connection with the signed network is illuminated. Taking advantage of this connection, a graph condition is proposed for the propagation model to converge. For the uniform scenario, necessary and sufficient conditions in terms of network topology are derived, which guarantee the convergence of the propagation model. Furthermore, if the signed network is structurally balanced, complementary probabilities will be achieved on the same opinion by the bipartite subgroups.