Summary: In  a generalized concatenated code was used to construct the t-fold unidirectional b-bit-byte error-correcting/d(dt)-fold unidirectional b-bit-byte error-detecting (t-UbEC/d(t)-UbED) codes. The concatenated code is to choose an inner code satisfying some disjoint sets and each set is a binary b-tuples unordered code. However,  gave five methods including trial and error to construct the optimal inner codes. Here, we present a systematic method for constructing the inner codes. It is shown that we can improve the coding efficiency for t-UbEC/d(t)-UbED) codes in some cases by using our inner codes.