  We prove that under a very general setting, a system of ODE passes the
Painleve test if and only if there is a good change of variable, such that the
pole singularity solutions are converted to regular power series, while the
converted ODE system is still kept regular. A consequence is that all principal
balances of an ODE system converge. We also prove that the results are natural
with respect to Hamiltonian systems.
