  The non-semisimple $gl(2|2)_k$ current superalgebra in the standard basis and
the corresponding non-unitary conformal field theory are investigated. Infinite
families of primary fields corresponding to all finite-dimensional irreducible
typical and atypical representations of $gl(2|2)$ and three (two even and one
odd) screening currents of the first kind are constructed explicitly in terms
of ten free fields.
