  4x4 Dirac (gamma) matrices (irreducible matrix representations of the
Clifford algebras C(3,1), C(1,3), C(4,0)) are an essential part of many
calculations in quantum physics. Although the final physical results do not
depend on the applied representation of the Dirac matrices (e.g. due to the
invariance of traces of products of Dirac matrices), the appropriate choice of
the representation used may facilitate the analysis. The present paper
introduces a particularly symmetric real representation of 4x4 Dirac matrices
(Majorana representation) which may prove useful in the future. As a byproduct,
a compact formula for (transformed) Pauli matrices is found. The consideration
is based on the role played by isoclinic 2-planes in the geometry of the real
Clifford algebra C(3,0) which provide an invariant geometric frame for it. It
can be generalized to larger Clifford algebras.
