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A modified algebraic decoding algorithm (ADA) is presented to decode up to five possible errors in a binary systematic (47, 24, 11) quadratic residue (QR) code. The main key points of the proposed ADA are to modify the erroneous conditions in Case 3, Case 4, and Case 5 of the ADA given in He et al. (2001) and to find out the true conditions from Case 2 to Case 5. The new conditions can also be applied to the ADA given in Lin et al. (2010). A simulation result shows that the decoding time of the proposed ADA is faster than that of ADA given in Lin et al. (2010).