  We study four dimensional $\kappa$-Minkowski spacetime constructed by the
twist deformation of $U(igl(4,R))$. We demonstrate that the differential
structure of such twist-deformed $\kappa$-Minkowski spacetime is closed in four
dimensions contrary to the construction of $\kappa$-Poincar\'{e} bicovariant
calculus which needs an extra fifth dimension. Our construction holds in
arbitrary dimensional spacetimes.
