In the past, the research on representation for synthesis systems had been focusing on two main issues, the completeness and the efficiency. There is, however, another important issue that is not addressed by most of traditional representation, the uniqueness. This report proposes a representation for synthesis called the Assignment Decision Diagram (ADD) that is complete, efficient and partially unique. In addition, the ADD can enrich the results of the synthesis. Discussion of ADD's properties and its uses in synthesis is provided in this report.