This paper describes an iterative algorithm for making Euclidean reconstruction of a scene from an image sequence captured by a camera with zero skew. The output consists of both the Euclidean reconstruction and the intrinsic parameters of the camera at the different imaging instants, i.e. it also provides a camera calibration. The problem is solved in two different steps. Firstly, the projective structure is obtained from a factorization method followed by a bundle adjustment method. Secondly, the Euclidean reconstruction is obtained from an iterative method that estimates the location of the absolute conic and the intrinsic parameters iteratively, using linear operations in each iteration. In this method a new constraint, called the orthogonality constraint, is used to constrain the absolute conic. Results are shown on experiments on both synthetic and real data.