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In recent years, the camera calibration using 1D patterns has been studied and improved by researchers all over the world. However, the progress in that area has been mainly in the sense of reducing the restrictions to the 1D pattern movement. On the other hand, the method's accuracy still demands improvements. In the present paper, the original technique proposed by Zhang is revisited and we demonstrate that the method's accuracy can be significantly improved, simply by analyzing and reformulating the problem. The numerical conditioning can be improved if a simple data normalization is performed. Furthermore, a non-linear solution based on the Partitioned Levenberg-Marquardt algorithm is proposed. That solution takes advantage of the problem's particular structure to reduce the computational complexity of the original method and to improve the accuracy. Tests using both synthetic and real images demonstrate that the calibration method using 1D patterns can be applied in practice, with accuracy comparable to other already traditional methods.