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We study a lattice model of an associating A–B binary mixture, which differs from the one originally proposed by Lin and Taylor (Phys. Rev. E, 1994, 49, 2058 and Phys. Rev. Lett., 1994, 73, 2863) because it allows interactions between all pairs of particles. This model can be mapped onto an Ising model with renormalized coupling parameters. The global phase diagram of the mixture is obtained as a function of the physical parameters. The appearance of closed loops of immiscibility is analysed in terms of the coupling parameters.