We introduce a construction of the differential calculus on the quantum supergroup GL(p,q)(1 parallel to 1). We obtain two differential calculi, respectively, associated with the left and the right Cartan-Maurer one-forms. We also obtain the quantum superalgebra of GL(p,q)(1 parallel to 1). Although all of the structures we obtain are derived without an R matrix, they nevertheless can be expressed using an R matrix. (C) 2000 American Institute of Physics. [S0022-2488(99)04910-5].