A new procedure for the reduction of Carte du Ciel plates is presented. A typical Carte du Ciel plate corresponding to the Bordeaux zone has been taken as an example. It shows triple exposures for each object and the modelling of the data has been performed by means of a non-linear least squares fitting of the sum of three bivariate Gaussian distributions. A number of solutions for the problems present in this kind of plates (optical aberrations, adjacency photographic effects, presence of grid lines, emulsion saturation) have been investigated. An internal accuracy of 0.1 in x and y was obtained for the position of each of the individual exposures. The external reduction to a catalogue led to results with an accuracy of 0.16 in x and 0.13 in y for the mean position of the three exposures. A photometric calibration has also been performed and magnitudes were determined with an accuracy of 0.09 mags.