; ;be a finite group of Lie type (e.g. ; ;) and ; ;a maximal unipotent subgroup of ; ;. If ; ;is a linear character of ; ;, then the unipotent Hecke algebra is ; ;. Unipotent Hecke algebras have a natural basis coming from double cosets of ; ;in ; ;. This paper describes relations for reducing products of basis elements, and gives a detailed description of the implications in the case ; ;.