RB-53-10 describes a method for fitting an orthogonal simple structure to a sample of vectors in k-space. This report extends the solution to the fitting of an oblique simple structure. Exactly k distinct oblique factors are obtained, and the contribution of each to 5 is at a relative maximum. The solution should be computationally feasible for moderately large values of k, given the resources of a digital computer like Illiac of the IBM 701. A numerical example is included in which k = 2. A generalized computer routine for a single-address, stored-program machine is also included.