  Let Cl1(1,3) and Cl2(1,3) be the subsets of elements of the Clifford algebra
Cl(1,3) of ranks 1 and 2 respectively. Recently it was proved that the subset
Cl2(p,q)+iCl1(p,q) of the complex Clifford algebra can be considered as a Lie
algebra. In this paper we prove that for p=1, q=3 the Lie algebra
Cl2(p,q)+iCl1(p,q) is isomorphic to the well known matrix Lie algebra sp(4,R)
of the symplectic Lie group Sp(4,R). Also we define the so called symplectic
group of Clifford algebra and prove that this Lie group is isomprphic to the
symplectic matrix group Sp(4,R).
