Abstract. For all previous constructions of 2 × 2 lattice space-time codes with a positive diversity product, the rank r(2) was such that r(2) ≤ 4. An example of a 2 × 2 lattice space-time code of rank 5 with a positive diversity product was given by Xing and Li. In this paper, we give an example of a 2 × 2 lattice space-time code of rank 8 with a positive diversity product. This gives an answer to the open problem set by Xing and Li.