  New approach to quantization of the relativistic Majorana field is presented.
It is based on expansion of the field into eigenfunctions of the axial momentum
-- a novel observable introduced recently. Relativistic invariance is used as
the main guiding principle instead of canonical formalism. Hidden structure of
the quantized Majorana field in the form of real Clifford algebra of Hermitian
fermionic operators is unveiled. Generators of the Poincar\'e transformations
in the Fock space are found as solutions of certain operator equations, without
invoking the principle of correspondence with classical conserved quantities.
Also operators of parity $\hat{\mbox{P}}$ and time reversal $\hat{\mbox{T}}$
are constructed.
