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The paper describes the implementation of a systolic array for a multilayer perceptron with a hardware-friendly learning algorithm. A pipelined modification of the on-line backpropagation algorithm is shown and explained. It better exploits the parallelism because both the forward and backward phases can be performed simultaneously. The neural network performance for the proposed modification is discussed and compared with the standard so-called on-line backpropagation algorithm in typical databases and with the various precisions required. Although the preliminary results are positive, subsequent theoretical analysis and further experiments with different training sets will be necessary. For this reason our VLSI systolic architecture—together with the combination of FPGA reconfiguration properties and a design flow based on generic VHDL—can create a reusable, flexible, and fast method of designing a complete ANN on a single FPGA and can permit very fast hardware verifications for our trials of the Pipeline On-line Backpropagation algorithm and the standard algorithms.