The authors improve a norm-relaxed method of strongly sub-feasible directions published in J.-B. Jian, H.-Y. Zheng, Q.-J. Hu and C.-M. Tang [Appl. Math. Comput. 182, No. 2, 955–976 (2006; Zbl 1108.65064)]. They introduce an active set technique to remove those constraints that are locally irrelevant and, therefore, the scale of the direction finding sub-problem is largely decreased. Instead of an explicit formula, they generate a high-order direction by solving a system of linear equations which also only includes the estimate of the active constraints and their gradients. The line search used in their algorithm combines the initialization and optimization processes meanwhile it prevents the objective value from increasing too much.