We demonstrate a new method to achieve the maximum singlet fraction using an entangled mixed two-qubit state as a resource. For this, we establish a tight upper bound on singlet fraction and show that the maximal singlet fraction obtained in Verstraete and Verschelde (Phys Rev Lett 90:097901(1)–097901(4), 2003) does not attain the upper bound on the singlet fraction derived here. Interestingly, we found that the required upper bound can, in fact, be achieved using local filtering operations. © 2016, Springer Science+Business Media New York.