Given a strictly increasing continuous function φ from [0, 1] to [0, 1] and its pseudo-inverse φ <Superscript>[−1]</Superscript>, conditions that φ must satisfy for C<Subscript> φ </Subscript>(x<Subscript>1</Subscript>, . . . ,x<Subscript>n</Subscript>)=φ <Superscript>[−1]</Superscript>(C(φ(x<Subscript>1</Subscript>), . . . ,φ(x<Subscript>n</Subscript>))) to be a copula for any copula C are studied. Some basic properties of the copulas obtained in...</subscript></subscript></superscript></subscript></subscript></subscript></superscript>