The More ´-Sorensen sequential (MSS) method computes the minimizer of a quadratic function defined by a limited-memory BFGS matrix subject to a two-norm trust-region constraint. This solver is an adaptation of the More ´-Sorensen direct method into an L-BFGS setting for large-scale optimization. The MSS method is a matrix-free iterative method that makes use of a recently proposed stable fast direct method for solving large shifted BFGS systems of equations. Numerical results will be presented.