One of the interesting problems of optimal indecomposable entanglement witnesses is whether there exists an optimal indecomposable entanglement witness which neither has the spanning property nor is associated with an extremal positive linear map. Here, we answer this question in the negative by examining the extremality of the positive linear maps constructed by Qi and Hou (2011 J. Phys. A: Math. Theor. 44 215305).