For determining motion/structure of a 3-D rigid object from point correspondences over two perspective views, a linear algorithm was developed in Refs. 3 and 4. This algorithm fails when the 3-D points under observation satisfy certain geometrical constraints, as demonstrated in Refs. 7 and 8. In the present paper, we show that the linear algorithm can be resurrected in these degenerate cases by adding additional lower order polynomial constraints to original equations.