In this paper we consider first the space-time as a principal bundle with structure group $SO(3,{\mathbb C})$ over the base $B={\mathbb R}^3$. From this viewpoint the 4-vector of velocity is replaced now by a $3\times 3$ orthogonal Hermitian matrix. Starting from the structure group $SO(3,{\mathbb C})$ the Lorentz transformations are written in 6 dimensions. Further it is considered a more sophisticated model of space-time with the same structural group $SO(3,{\mathbb C})$ over the base $SO(3,{\mathbb R})$. In this model there are only rotations, but no translations. So the Lorentz transformations are also converted for this bundle.