In the computation of the three-dimensional structure, it has been demonstrated by many authors that introducing a third camera provides improvement over the use of two views only. In this paper, we propose a new algebraic derivation for the projection matrix of the third camera. This derivation is obtained by using the relationships between the projection matrices, the epipolar geometry and the trilinear tensors. Compared to previous methods, our method has the advantage to work in the special case where the camera centers are collinear. In addition, it has the advantage of simplicity and it is very straightforward to implement since it is a linear method. In our experiments, we have used view synthesis to highlight the quality of the computed projective structure. Our tests have been performed on both synthetic and real data.