Fuzzy relational equations have played an important role in fuzzy modeling and applied to many practical problems. Most theories of fuzzy relational equations based on a premise that the solution set is not empty. However, this is often not the case in practical applications. Recently, Chakraborty et al. presented an efficient algorithm to solve the best approximate solution for the fuzzy relational equations, XoA=I, with max-min composition, where I denotes the identity matrix. In this paper, new theoretical results are proposed for solving this particular problem. Hence, one simple procedure can be presented to find the best approximate solution quickly. A numerical example is provided to illustrate the procedure.