  The Lyapunov Characteristic Exponents are a useful indicator of chaos in
astronomical dynamical systems. They are usually computed through a standard,
very efficient and neat algorithm published in 1980. However, for Hamiltonian
systems the expected result of pairs of opposite exponents is not always
obtained with enough precision. We find here why in these cases the initial
order of the deviation vectors matters, and how to sort them in order to obtain
a correct result.
