  We construct quantum deformation of Poincar\'e group using as a starting
point $SU(2,2)$ conformal group and twistor-like definition of the Minkowski
space. We obtain quantum deformation of $SU(2,2)$ as a real form of
multiparametric $GL(4,C)_{q_{ij},r}$. It is shown that Poincar\'e subgroup
exists for special nonstandard one-parametric deformation only, the deformation
parameter $r$ being equal to unity. This leads to commuting affine structure of
the corresponding Minkowski space and simple structure of the corresponding Lie
algebra, the deformation of the group being non-trivial.
