This paper attempts to establish a theory for a general auto-associative memory model. We start by defining a new concept called supporting function to replace the concept of energy function. The latter relies on an assumption of symmetric connection weights, which is used in the conventional Hopfield auto-associative memory, but not evidenced in any biological memories. We then formulate the information retrieval or recalling process as a dynamic system by making use of the supporting function, explore its stability and attraction conditions, and develop an algorithm for learning the attraction condition based upon Rosenblatt's perceptron rule. The effectiveness of the learning algorithm is evidenced by some outstanding experiment results.