Let ; ; 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 ; ; .