  In the present paper we construct all typical finite-dimensional
representations of the quantum Lie superalgebra $U_{q}[gl(2/2)]$ at generic
deformation parameter $q$. As in the non-deformed case the finite-dimensional
$U_{q}[gl(2/2)]$-module $W^{q}$ obtained is irreducible and can be decomposed
into finite-dimensional irreducible $U_{q}[gl(2)\oplus gl(2)]$-submodules
$V^{q}_{k}$
