In this paper, a design procedure is presented for synthesizing associative memories based on the Brain-State-in-a-Box neural network model. The theoretical analysis herein guarantees that the desired memory patterns are stored as asymptotically stable equilibrium points with very few spurious states. In order to avoid extensive computation, learning and forgetting are utilized by adding patterns to be stored as asymptotically stable equilibrium points to an existing set of stored patterns and deleting specified patterns from a given set of stored patterns without affecting the rest in a given network. Furthermore, the number of the memorized patterns in a designed Brain-State-in-a-Box neural network model can be made much more than that of neurons. Simulation results demonstrate the validity and characteristics of the proposed approach.