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We propose a memory-based naming game (MBNG) model with two-state variables in fun-connected networks, which is like some previous opinion propagation models. It is found that this model is deeply affected by the memory decision parameter, and then its dynamical behaviour can be partly analysed by using numerical simulation and analytical argument. We also report a modified MBNG model with the forgetting curve of Ebbinghaus in the memory. With deletion of one parameter in the MBNG model, it can converge to success rate S(t) = 1 and the average sum E(t) is decided by the size of network N.