This paper proposes a general model for bidirectional associative memories that associate patterns between the X-space and the Y-space. The general model does not require the usual assumption that the interconnection weight from a neuron in the X-space to a neuron in the Y-space is the same as the one from the Y-space to the X-space. We start by defining a supporting function to measure how well a state supports another state in a general bidirectional associative memory (GBAM). We then use the supporting function to formulate the associative recalling process as a dynamic system, explore its stability and asymptotic stability conditions, and develop an algorithm for learning the asymptotic stability conditions using the Rosenblatt perceptron rule. The effectiveness of the proposed model for recognition of noisy patterns and the performance of the model in terms of storage capacity, attraction, and spurious memories are demonstrated by some outstanding experimental results.