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An iterative learning algorithm called PRLAB is described for the discrete bidirectional associative memory (BAM). Guaranteed recall of all training pairs is ensured by PRLAB. The proposed algorithm is significant in many ways. Unlike many existing iterative learning algorithms, PRLAB is not based on the gradient descent technique. It is a novel adaptation from the well-known relaxation method for solving a system of linear inequalities. The algorithm is very fast. Learning 200 random patterns in a 200-200 BAM takes only 20 epochs on the average. PRLAB is highly insensitive to learning parameters and the initial configuration of a BAM. It also offers high scalability for large applications by providing the same high performance when the number of training patterns are increased in proportion to the size of the BAM. An extensive performance analysis of the new learning algorithm is included