  We introduce a construction of the differential calculus on the quantum
supergroup GL$_{p,q}(1| 1)$. We obtain two differential calculi, respectively,
associated with the left and right Cartan-Maurer one-forms. We also obtain the
quantum superalgebra of GL$_{p,q}(1| 1)$. Although all of the structures we
obtain are derived without an R matrix, they neverthless can be expressed using
an R matrix.
