This paper extends the relational algebra of data bases, presented by Codd [4] and others, in four areas. The first is the use of selector names to remove order dependencies from the columns of a relation. This use of selector names enables us to define a more general class of operations, which include the normal relational operations of union, equi-join etc., as special cases. Thirdly we introduce relations represented algorithmically as well as by a stored set of tuples. Such computed relations cannot always be effectively realised as a finite set of tuples. Finally we consider relational expressions as algorithmic representations of relations and characterize their effectiveness.