We provide an alternate representation to the result that the Lie algebra of generators of the system of n differential equations, ( y a ) ″ = 0 , is isomorphic to the Lie algebra of the special linear group of order ( n + 2 ) , over the real numbers, s l ( n + 2 , ℝ ) . In this paper, we provide an alternate representation of the symmetry algebra by simple relabelling of indices. This provides one more proof of the result that the symmetry algebra of ( y a ) ″ = 0 is s l ( n + 2 , ℝ ) .