A relational database is a database based on the relational model.
Strictly speaking, this means a relational database takes the form of a specific collection of data. The database software that is used to manage the data is called a relational database management system, or RDBMS. (However, common usage doesn't always preserve this distinction.)
Relational databases should be stored in normal form.
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This article contains material from relational database at FOLDOC; used with permission.