Determining the structure of the world and the motion of the observer from image changes has been a central problem in computer vision for over fifteen years. Since the early work on Structure from Motion (SFM) by Longuet-Higgins and Pradzny, several techniques have been developed to compute the motion of the camera, the shape of moving objects, or distances to points in the world. However, the image changes are non-linearly related to camera motion and distances to points in the world. Thus, solving the problem typically requires non-linear optimization techniques that can be unstable or computationally inefficient. Linear algorithms are preferable since they are computationally advantageous, and since linear estimation is much better understood than non-linear estimation. Our paper describes an unbiased, completely linear algorithm for Structure-from-Motion. This work is similar to that of Jepson and Heeger except that we employ spherical projection. The use of a spherical imaging geometry allows a simpler and more intuitive derivation of the algorithm, and produces an unbiased estimator. Experimental results are provided that demonstrate the performance of the algorithm.