  Following the construction of the $\kappa$-Minkowski space from the
bicrossproduct structure of the $\kappa$-Poincare group, we investigate
possible differential calculi on this noncommutative space. We discuss then the
action of the Lorentz quantum algebra and prove that there are no 4D
bicovariant differential calculi, which are Lorentz covariant. We show,
however, that there exist a five-dimensional differential calculus, which
satisfies both requirements. We study also a toy example of 2D
$\kappa$-Minkowski space and and we briefly discuss the main properties of its
differential calculi.
