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In this paper, a new algorithm for a cubic spline fit with equally spaced data points and given end conditions is described. It provides a new understanding of how a spline fit works and possesses the following computational advantages: 1) It can solve large size problems (virtually unlimited). 2) The accuracy can be realistically controlled based on the characteristics of data. 3) The computation time-is linearly proportional to the size of the problem. 4) It can handle a localized fit. 4) It can handle a localizd. The new algorithm is particularly suitable to be implemented in minicomputers for cutting surfaces by numerically controlled machines and for other applications.