In 1980, Han 6] described a nitely terminating algorithm for solving a system Ax b of linear inequalities in a least squares sense. The algorithm uses a singular value decomposition of a submatrix of A on each iteration, making it impractical for all but the smallest problems. This paper shows that a modi cation of Han's algorithm allows the iterates to be computed using QR factorization with column pivoting, which signi cantly reduces the computational cost and allows e cient updating/downdating techniques to be used. The e ectiveness of this modi cation is demonstrated, implementation details are given, and the behaviour of the algorithm discussed. Theoretical and numerical results are shown from the application of the algorithm to linear separability problems.