We consider the relationship between ideals of a BCI-algebra and order ideals of its adjoint semigroup. We show that (1) if I is an ideal, then I=M1(M(I)), (2) M(M1(J)) is the order ideal generated by JR(X), (3) if X is a BCK-algebra, then J=M(M1(J)) for any order ideal J of X, thus, for each BCK-algebra X there is a one-to-one correspondence between the set (X) of all ideals of X and the set 𝒪(X) of all order ideals of it, and (4) the order M(M1(J)) is an order ideal if and only if M1(J) is an ideal. These results are the generalization of those denoted by Huang and Wang (1995) and Li (1999). We can answer the open problem of Li affirmatively.