It is widely acknowledged that pursuing solely convenience causes such problems as excluding users, spoiling users ability, and so on. Inconvenient systems and methods provide users with such benefits as enhancing awareness and allowing creative contribution. However, the systematic way for implementing such benefits is now unknown. Focusing on the contradiction between convenience and such benefits, this paper introduces the contradiction matrix that is a method of TRIZ for inventive problem solving. By analyzing many inconvenient tools and methods, some principles, which relate inconvenience and their benefits, are derived and are placed in what we call fuben-eki (FUrther BENEfit of a Kind of Inconvenience) matrix. This paper demonstrates the way for utilizing the matrix, just like the contradiction matrix of TRIZ, for supporting idea generation of implementing benefits of inconvenience.