Most real-world negotiation involves multiple interdependent issues, which makes an agent’s utility functions nonlinear. Traditional negotiation mechanisms, which were designed for linear utilities, do not fare well in nonlinear contexts. One of the main challenges in developing effective nonlinear negotiation protocols is scalability; they cannot find a high-quality solution when there are many issues, due to computational intractability. One reasonable approach to reducing computational cost, while maintaining good quality outcomes, is to decompose the utility space into several largely independent subspaces. In this paper, we propose a method for decomposing a utility space based on every agent’s utility space. In addition, the mediator finds the contracts in each group based on the votes from all agents, and combines the contract in each issue-group. This method allows good outcomes with greater scalability than the method without issue-grouping. We demonstrate that our protocol, based on issue-groups, has a higher optimality rate than previous efforts, and discuss the impact on the optimality of the negotiation outcomes.