  The differential calculus on the quantum supergroup GL$_q(1| 1)$ was
introduced by Schmidke {\it et al}. (1990 {\it Z. Phys. C} {\bf 48} 249). We
construct a differential calculus on the quantum supergroup GL$_q(1| 1)$ in a
different way and we obtain its quantum superalgebra. The main structures are
derived without an R-matrix. It is seen that the found results can be written
with help of a matrix $\hat{R}$
