In a recent paper we introduced an accelerated version of the Successive Orthogonal Projections method which seems to be useful for solving some classes of large scale linear feasibility problems. The main step of the method involves an orthogonal projection on a linear manifold Bx = b. In this note we consider the very frequent situation where the m X m identity matrix is a submatrix of B. We develop a procedure for computing the projection which only involves "small" matrix factorizations. © 1988.13259261George, Heath, Solution of Sparse Linear Least Squares Problems using Givens Rotations (1980) Linear Algebra and Its Applications, 34, pp. 68-83Golub, Van Loan, (1985) Matrix Computations, , John Hopkins University Press, Baltimore, MDMartinez, An Accelerated Successive Orthogonal Projection Method for Solving Large Scale Linear Feasibility Problems (1988) Computers and Mathematics with Applications, , (to appear)