We study Majorana‐like constructs in the (1/2, 0) ⊕ (0, 1/2) representation. We show that the parity properties of a fermion and its antifermion are quite different comparing with the Dirac case. The transformation laws for C and T operations have also been given on the secondary quantization level. The construct can be applied to explanation of the present situation in neutrino physics. The case of the (1, 0) ⊕ (0, 1) field is also considered.