3D scene information can be extracted from images acquired by cameras. Before doing the actual reconstruction, camera calibration has to be done. Reconstruction accuracy is highly dictated by the calibration. Two typical demands, which are not easily simultaneously satisfied, are: calibration has to be done in a fast and convenient manner and yet assure a high degree of reconstruction accuracy. The computational part of calibration usually includes the initialization of camera parameters and refinement based on an initial set of values. The goodness of the initial set greatly affects the refinement procedure in terms of convergence speed and ultimately reconstruction accuracy. This work proposes a new calibration method for 3D kinematic systems. It shortens the commonly used calibration procedure, gives better initial parameter values for the refinement procedure which in turn is supposed to assure faster and safer convergence of the iterative minimization algorithm. Additionally, it is shown that even without parameter refinement the proposed method gives more accurate 3D reconstruction output.