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In this paper, new equations for the self-calibration of a moving camera with unchanged intrinsic parameters are proposed. Unlike most existing methods that require solving equations in three or more unknowns, our equations are only bivariate. The two unknowns, in our equations, are the scale factors that are responsible for the nonlinearity of Kruppa's equations due to a triplet of images. Once the scale factors are calculated, Kruppa's coefficients are linearly retrieved. The results of our experiments, conducted on simulated and real data, are also presented.