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Typical bidirectional associative memories (BAM) use an offline, one-shot learning rule, have poor memory storage capacity, are sensitive to noise, and are subject to spurious steady states during recall. Recent work on BAM has improved network performance in relation to noisy recall and the number of spurious attractors, but at the cost of an increase in BAM complexity. In all cases, the networks can only recall bipolar stimuli and, thus, are of limited use for grey-level pattern recall. In this paper, we introduce a new bidirectional heteroassociative memory model that uses a simple self-convergent iterative learning rule and a new nonlinear output function. As a result, the model can learn online without being subject to overlearning. Our simulation results show that this new model causes fewer spurious attractors when compared to others popular BAM networks, for a comparable performance in terms of tolerance to noise and storage capacity. In addition, the novel output function enables it to learn and recall grey-level patterns in a bidirectional way.