In this paper, we propose a new factorizationbased algorithm for projective reconstruction by minimizing the 2D reprojection error in multiple images. Reformulating the projective reconstruction problem into a constrained minimization one, we estimate the projective depths, the projection matrix and the projective motion together by the solving a sequence of unconstrained minimization problems using the augmented Lagrangian method. The proposed algorithm is ready to handle missing data and it is guaranteed to converge more robustly and rapidly than the algorithm of [6].