  Several issues concerning quantum kappa-Poincare algebra are discussed and
reconsidered here. We propose two different formulations of kappa-Poincare
quantum algebra. Firstly we present a complete Hopf algebra formulae of
kappa-Poincare in classical Poincare basis. Further by adding one extra
generator, which modifies the classical structure of Poincare algebra, we
eliminate non polynomial functions in the kappa-parameter. Hilbert space
representations of such algebras make Doubly Special Relativity (DSR) similar
to the Stueckelberg's version of (proper-time) relativistic Quantum Mechanics.
