This short note aims to make some modification for improving the results presented in [1]. A. Ghodousian et al. discussed the resolution of a system of max-Dubois-Prade fuzzy relation equations based on their proposed index sets J_i, i ∈ I. It is found that not every e ∈ E = J₁ × J₂ × unmapped: inline-formula unmapped: math unmapped: mo ⋯unmapped: mspace × J_m corresponds to a solution. To overcome this flaw, we modify the expression of the index sets, denoted by J⁼_i , i ∈ I. Based on the modified index sets, resolution of the max-Dubois-Prade fuzzy relation equations becomes easier, regarding the computational cost.