In a typical brainstorming method, criticism must be withheld for creative ideation. We envisage a web-based system that is designed to avoid possible negative influences of, and make good use of, critical thinking to generate creative ideas. To investigate its plausibility, we developed a system in which people participate collectively in a sequence of processes including generating, criticizing, modifying, and evaluating creative ideas. Here we report the results from conducting an experiment with 238 participants to compare the critical thinking (CT) design with a criticizing phase against the brainstorming (BS) design without it. The main finding was that the CT design resulted in the generation of higher quality ideas than the BS design without sacrificing fluency with respect to response time and the number of characters.