  The completeness of the group classification of systems of two linear
second-order ordinary differential equations with constant coefficients is
delineated in the paper. The new cases extend what has been done in the
literature. These cases correspond to the type of equations where the
commutative property of the coefficient matrices with respect to the dependent
variables and the first-order derivatives in the considered system does not
hold. A discussion of the results as well as a note on the extension to linear
systems of second-order ordinary differential equations with more than two
equations are given.
