In this paper, we study d-primitive words and D(1)-concatenated words. First we show that neither D(1), the set of all d-primitive words, nor D(1)D(1), the set of all D(1)-concatenated words, is regular. Next we show that for u, v, w ∈Σ+ with |u|=|w|, uvw ∈ D(1) if and only if uv+w ⊆ D(1). It is also shown that every d-primitive word, with the length of two or more, is D(1)-concatenated.