  We present the consistent approach to finding the discrete transformations in
the representation spaces of the proper Poincar\'e group. To this end we use
the possibility to establish a correspondence between involutory automorphisms
of the proper Poincar\'e group and the discrete transformations. As a result,
we derive rules of the discrete transformations for arbitrary spin-tensor
fields without the use of relativistic wave equations. Besides, we construct
explicitly fields carrying representations of the extended Poincar\'e group,
which includes the discrete transformations as well.
