  The symmetries provided by representations of the centrally extended Lie
superalgebra $\mathfrak{psl}(2|2)$ are known to play an important role in the
spin chain models originated in the planar anti-de Sitter/conformal field
theory correspondence and one-dimensional Hubbard model. We give a complete
description of finite-dimensional irreducible representations of this
superalgebra thus extending the work of Beisert which deals with a generic
family of representations. Our description includes a new class of modules with
degenerate eigenvalues of the central elements. Moreover, we construct explicit
bases in all irreducible representations by applying the techniques of
Mickelsson--Zhelobenko algebras.
