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A noise process with piecewise constant sample functions in the form of a finite random Walsh series is proposed, and its properties and potential usefulness in computations is analyzed. It is shown that the infinite series yields the familiar white noise model and that its integral yields a Wiener process almost surely. The integrated process also has all the properties of a Wiener process (modulo the sample points) in the finite series expansion. Using the stochastic calculus developed by McShane , , the necessary framework for handling stochastic system models driven by Walsh noise is developed.